1,1,94,0,0.0724306,"\int \left(a+b x^3\right) \left(c+d x^3\right)^4 \, dx","Int[(a + b*x^3)*(c + d*x^3)^4,x]","\frac{2}{7} c^2 d x^7 (3 a d+2 b c)+\frac{1}{4} c^3 x^4 (4 a d+b c)+\frac{1}{13} d^3 x^{13} (a d+4 b c)+\frac{1}{5} c d^2 x^{10} (2 a d+3 b c)+a c^4 x+\frac{1}{16} b d^4 x^{16}","\frac{2}{7} c^2 d x^7 (3 a d+2 b c)+\frac{1}{4} c^3 x^4 (4 a d+b c)+\frac{1}{13} d^3 x^{13} (a d+4 b c)+\frac{1}{5} c d^2 x^{10} (2 a d+3 b c)+a c^4 x+\frac{1}{16} b d^4 x^{16}",1,"a*c^4*x + (c^3*(b*c + 4*a*d)*x^4)/4 + (2*c^2*d*(2*b*c + 3*a*d)*x^7)/7 + (c*d^2*(3*b*c + 2*a*d)*x^10)/5 + (d^3*(4*b*c + a*d)*x^13)/13 + (b*d^4*x^16)/16","A",2,1,17,0.05882,1,"{373}"
2,1,70,0,0.0426525,"\int \left(a+b x^3\right) \left(c+d x^3\right)^3 \, dx","Int[(a + b*x^3)*(c + d*x^3)^3,x]","\frac{1}{4} c^2 x^4 (3 a d+b c)+\frac{1}{10} d^2 x^{10} (a d+3 b c)+\frac{3}{7} c d x^7 (a d+b c)+a c^3 x+\frac{1}{13} b d^3 x^{13}","\frac{1}{4} c^2 x^4 (3 a d+b c)+\frac{1}{10} d^2 x^{10} (a d+3 b c)+\frac{3}{7} c d x^7 (a d+b c)+a c^3 x+\frac{1}{13} b d^3 x^{13}",1,"a*c^3*x + (c^2*(b*c + 3*a*d)*x^4)/4 + (3*c*d*(b*c + a*d)*x^7)/7 + (d^2*(3*b*c + a*d)*x^10)/10 + (b*d^3*x^13)/13","A",2,1,17,0.05882,1,"{373}"
3,1,50,0,0.0284518,"\int \left(a+b x^3\right) \left(c+d x^3\right)^2 \, dx","Int[(a + b*x^3)*(c + d*x^3)^2,x]","\frac{1}{7} d x^7 (a d+2 b c)+\frac{1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac{1}{10} b d^2 x^{10}","\frac{1}{7} d x^7 (a d+2 b c)+\frac{1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac{1}{10} b d^2 x^{10}",1,"a*c^2*x + (c*(b*c + 2*a*d)*x^4)/4 + (d*(2*b*c + a*d)*x^7)/7 + (b*d^2*x^10)/10","A",2,1,17,0.05882,1,"{373}"
4,1,28,0,0.0126816,"\int \left(a+b x^3\right) \left(c+d x^3\right) \, dx","Int[(a + b*x^3)*(c + d*x^3),x]","\frac{1}{4} x^4 (a d+b c)+a c x+\frac{1}{7} b d x^7","\frac{1}{4} x^4 (a d+b c)+a c x+\frac{1}{7} b d x^7",1,"a*c*x + ((b*c + a*d)*x^4)/4 + (b*d*x^7)/7","A",2,1,15,0.06667,1,"{373}"
5,1,144,0,0.0937481,"\int \frac{a+b x^3}{c+d x^3} \, dx","Int[(a + b*x^3)/(c + d*x^3),x]","\frac{(b c-a d) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{4/3}}-\frac{(b c-a d) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{4/3}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{4/3}}+\frac{b x}{d}","\frac{(b c-a d) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{4/3}}-\frac{(b c-a d) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{4/3}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{4/3}}+\frac{b x}{d}",1,"(b*x)/d + ((b*c - a*d)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*d^(4/3)) - ((b*c - a*d)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(2/3)*d^(4/3)) + ((b*c - a*d)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(2/3)*d^(4/3))","A",7,7,17,0.4118,1,"{388, 200, 31, 634, 617, 204, 628}"
6,1,169,0,0.082311,"\int \frac{a+b x^3}{\left(c+d x^3\right)^2} \, dx","Int[(a + b*x^3)/(c + d*x^3)^2,x]","-\frac{(2 a d+b c) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{18 c^{5/3} d^{4/3}}+\frac{(2 a d+b c) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{9 c^{5/3} d^{4/3}}-\frac{(2 a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} d^{4/3}}-\frac{x (b c-a d)}{3 c d \left(c+d x^3\right)}","-\frac{(2 a d+b c) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{18 c^{5/3} d^{4/3}}+\frac{(2 a d+b c) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{9 c^{5/3} d^{4/3}}-\frac{(2 a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} d^{4/3}}-\frac{x (b c-a d)}{3 c d \left(c+d x^3\right)}",1,"-((b*c - a*d)*x)/(3*c*d*(c + d*x^3)) - ((b*c + 2*a*d)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(3*Sqrt[3]*c^(5/3)*d^(4/3)) + ((b*c + 2*a*d)*Log[c^(1/3) + d^(1/3)*x])/(9*c^(5/3)*d^(4/3)) - ((b*c + 2*a*d)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(18*c^(5/3)*d^(4/3))","A",7,7,17,0.4118,1,"{385, 200, 31, 634, 617, 204, 628}"
7,1,197,0,0.1063946,"\int \frac{a+b x^3}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)/(c + d*x^3)^3,x]","-\frac{(5 a d+b c) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{54 c^{8/3} d^{4/3}}+\frac{(5 a d+b c) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{27 c^{8/3} d^{4/3}}-\frac{(5 a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{9 \sqrt{3} c^{8/3} d^{4/3}}+\frac{x (5 a d+b c)}{18 c^2 d \left(c+d x^3\right)}-\frac{x (b c-a d)}{6 c d \left(c+d x^3\right)^2}","-\frac{(5 a d+b c) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{54 c^{8/3} d^{4/3}}+\frac{(5 a d+b c) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{27 c^{8/3} d^{4/3}}-\frac{(5 a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{9 \sqrt{3} c^{8/3} d^{4/3}}+\frac{x (5 a d+b c)}{18 c^2 d \left(c+d x^3\right)}-\frac{x (b c-a d)}{6 c d \left(c+d x^3\right)^2}",1,"-((b*c - a*d)*x)/(6*c*d*(c + d*x^3)^2) + ((b*c + 5*a*d)*x)/(18*c^2*d*(c + d*x^3)) - ((b*c + 5*a*d)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(9*Sqrt[3]*c^(8/3)*d^(4/3)) + ((b*c + 5*a*d)*Log[c^(1/3) + d^(1/3)*x])/(27*c^(8/3)*d^(4/3)) - ((b*c + 5*a*d)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(54*c^(8/3)*d^(4/3))","A",8,8,17,0.4706,1,"{385, 199, 200, 31, 634, 617, 204, 628}"
8,1,122,0,0.0710383,"\int \left(a+b x^3\right)^2 \left(c+d x^3\right)^3 \, dx","Int[(a + b*x^3)^2*(c + d*x^3)^3,x]","\frac{1}{10} d x^{10} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{7} c x^7 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 x+\frac{1}{4} a c^2 x^4 (3 a d+2 b c)+\frac{1}{13} b d^2 x^{13} (2 a d+3 b c)+\frac{1}{16} b^2 d^3 x^{16}","\frac{1}{10} d x^{10} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{7} c x^7 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 x+\frac{1}{4} a c^2 x^4 (3 a d+2 b c)+\frac{1}{13} b d^2 x^{13} (2 a d+3 b c)+\frac{1}{16} b^2 d^3 x^{16}",1,"a^2*c^3*x + (a*c^2*(2*b*c + 3*a*d)*x^4)/4 + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^7)/7 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^10)/10 + (b*d^2*(3*b*c + 2*a*d)*x^13)/13 + (b^2*d^3*x^16)/16","A",2,1,19,0.05263,1,"{373}"
9,1,82,0,0.0460077,"\int \left(a+b x^3\right)^2 \left(c+d x^3\right)^2 \, dx","Int[(a + b*x^3)^2*(c + d*x^3)^2,x]","\frac{1}{7} x^7 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 x+\frac{1}{5} b d x^{10} (a d+b c)+\frac{1}{2} a c x^4 (a d+b c)+\frac{1}{13} b^2 d^2 x^{13}","\frac{1}{7} x^7 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 x+\frac{1}{5} b d x^{10} (a d+b c)+\frac{1}{2} a c x^4 (a d+b c)+\frac{1}{13} b^2 d^2 x^{13}",1,"a^2*c^2*x + (a*c*(b*c + a*d)*x^4)/2 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^7)/7 + (b*d*(b*c + a*d)*x^10)/5 + (b^2*d^2*x^13)/13","A",2,1,19,0.05263,1,"{373}"
10,1,50,0,0.0292321,"\int \left(a+b x^3\right)^2 \left(c+d x^3\right) \, dx","Int[(a + b*x^3)^2*(c + d*x^3),x]","a^2 c x+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{4} a x^4 (a d+2 b c)+\frac{1}{10} b^2 d x^{10}","a^2 c x+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{4} a x^4 (a d+2 b c)+\frac{1}{10} b^2 d x^{10}",1,"a^2*c*x + (a*(2*b*c + a*d)*x^4)/4 + (b*(b*c + 2*a*d)*x^7)/7 + (b^2*d*x^10)/10","A",2,1,17,0.05882,1,"{373}"
11,1,173,0,0.1284591,"\int \frac{\left(a+b x^3\right)^2}{c+d x^3} \, dx","Int[(a + b*x^3)^2/(c + d*x^3),x]","-\frac{(b c-a d)^2 \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{7/3}}+\frac{(b c-a d)^2 \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{7/3}}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{7/3}}-\frac{b x (b c-2 a d)}{d^2}+\frac{b^2 x^4}{4 d}","-\frac{(b c-a d)^2 \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{7/3}}+\frac{(b c-a d)^2 \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{7/3}}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{7/3}}-\frac{b x (b c-2 a d)}{d^2}+\frac{b^2 x^4}{4 d}",1,"-((b*(b*c - 2*a*d)*x)/d^2) + (b^2*x^4)/(4*d) - ((b*c - a*d)^2*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*d^(7/3)) + ((b*c - a*d)^2*Log[c^(1/3) + d^(1/3)*x])/(3*c^(2/3)*d^(7/3)) - ((b*c - a*d)^2*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(2/3)*d^(7/3))","A",8,7,19,0.3684,1,"{390, 200, 31, 634, 617, 204, 628}"
12,1,203,0,0.2436476,"\int \frac{\left(a+b x^3\right)^2}{\left(c+d x^3\right)^2} \, dx","Int[(a + b*x^3)^2/(c + d*x^3)^2,x]","\frac{(b c-a d) (a d+2 b c) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{9 c^{5/3} d^{7/3}}-\frac{2 (b c-a d) (a d+2 b c) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{9 c^{5/3} d^{7/3}}+\frac{2 (b c-a d) (a d+2 b c) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} d^{7/3}}+\frac{x (b c-a d)^2}{3 c d^2 \left(c+d x^3\right)}+\frac{b^2 x}{d^2}","\frac{(b c-a d) (a d+2 b c) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{9 c^{5/3} d^{7/3}}-\frac{2 (b c-a d) (a d+2 b c) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{9 c^{5/3} d^{7/3}}+\frac{2 (b c-a d) (a d+2 b c) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} d^{7/3}}+\frac{x (b c-a d)^2}{3 c d^2 \left(c+d x^3\right)}+\frac{b^2 x}{d^2}",1,"(b^2*x)/d^2 + ((b*c - a*d)^2*x)/(3*c*d^2*(c + d*x^3)) + (2*(b*c - a*d)*(2*b*c + a*d)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(3*Sqrt[3]*c^(5/3)*d^(7/3)) - (2*(b*c - a*d)*(2*b*c + a*d)*Log[c^(1/3) + d^(1/3)*x])/(9*c^(5/3)*d^(7/3)) + ((b*c - a*d)*(2*b*c + a*d)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(9*c^(5/3)*d^(7/3))","A",9,8,19,0.4211,1,"{390, 385, 200, 31, 634, 617, 204, 628}"
13,1,258,0,0.2327368,"\int \frac{\left(a+b x^3\right)^2}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^2/(c + d*x^3)^3,x]","-\frac{\left(5 a^2 d^2+2 a b c d+2 b^2 c^2\right) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{54 c^{8/3} d^{7/3}}+\frac{\left(5 a^2 d^2+2 a b c d+2 b^2 c^2\right) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{27 c^{8/3} d^{7/3}}-\frac{\left(5 a^2 d^2+2 a b c d+2 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{9 \sqrt{3} c^{8/3} d^{7/3}}-\frac{x (b c-a d) (5 a d+4 b c)}{18 c^2 d^2 \left(c+d x^3\right)}-\frac{x \left(a+b x^3\right) (b c-a d)}{6 c d \left(c+d x^3\right)^2}","-\frac{\left(5 a^2 d^2+2 a b c d+2 b^2 c^2\right) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{54 c^{8/3} d^{7/3}}+\frac{\left(5 a^2 d^2+2 a b c d+2 b^2 c^2\right) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{27 c^{8/3} d^{7/3}}-\frac{\left(5 a^2 d^2+2 a b c d+2 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{9 \sqrt{3} c^{8/3} d^{7/3}}-\frac{x (b c-a d) (5 a d+4 b c)}{18 c^2 d^2 \left(c+d x^3\right)}-\frac{x \left(a+b x^3\right) (b c-a d)}{6 c d \left(c+d x^3\right)^2}",1,"-((b*c - a*d)*x*(a + b*x^3))/(6*c*d*(c + d*x^3)^2) - ((b*c - a*d)*(4*b*c + 5*a*d)*x)/(18*c^2*d^2*(c + d*x^3)) - ((2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(9*Sqrt[3]*c^(8/3)*d^(7/3)) + ((2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*Log[c^(1/3) + d^(1/3)*x])/(27*c^(8/3)*d^(7/3)) - ((2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(54*c^(8/3)*d^(7/3))","A",8,8,19,0.4211,1,"{413, 385, 200, 31, 634, 617, 204, 628}"
14,1,252,0,0.1914622,"\int \frac{\left(c+d x^3\right)^4}{a+b x^3} \, dx","Int[(c + d*x^3)^4/(a + b*x^3),x]","\frac{d^2 x^4 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right)}{4 b^3}+\frac{d x (2 b c-a d) \left(a^2 d^2-2 a b c d+2 b^2 c^2\right)}{b^4}-\frac{(b c-a d)^4 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{13/3}}+\frac{(b c-a d)^4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{13/3}}-\frac{(b c-a d)^4 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{13/3}}+\frac{d^3 x^7 (4 b c-a d)}{7 b^2}+\frac{d^4 x^{10}}{10 b}","\frac{d^2 x^4 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right)}{4 b^3}+\frac{d x (2 b c-a d) \left(a^2 d^2-2 a b c d+2 b^2 c^2\right)}{b^4}-\frac{(b c-a d)^4 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{13/3}}+\frac{(b c-a d)^4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{13/3}}-\frac{(b c-a d)^4 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{13/3}}+\frac{d^3 x^7 (4 b c-a d)}{7 b^2}+\frac{d^4 x^{10}}{10 b}",1,"(d*(2*b*c - a*d)*(2*b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/b^4 + (d^2*(6*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*x^4)/(4*b^3) + (d^3*(4*b*c - a*d)*x^7)/(7*b^2) + (d^4*x^10)/(10*b) - ((b*c - a*d)^4*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(13/3)) + ((b*c - a*d)^4*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(13/3)) - ((b*c - a*d)^4*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(13/3))","A",8,7,19,0.3684,1,"{390, 200, 31, 634, 617, 204, 628}"
15,1,208,0,0.1476991,"\int \frac{\left(c+d x^3\right)^3}{a+b x^3} \, dx","Int[(c + d*x^3)^3/(a + b*x^3),x]","\frac{d x \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3}-\frac{(b c-a d)^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{10/3}}+\frac{(b c-a d)^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{10/3}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{10/3}}+\frac{d^2 x^4 (3 b c-a d)}{4 b^2}+\frac{d^3 x^7}{7 b}","\frac{d x \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3}-\frac{(b c-a d)^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{10/3}}+\frac{(b c-a d)^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{10/3}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{10/3}}+\frac{d^2 x^4 (3 b c-a d)}{4 b^2}+\frac{d^3 x^7}{7 b}",1,"(d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x)/b^3 + (d^2*(3*b*c - a*d)*x^4)/(4*b^2) + (d^3*x^7)/(7*b) - ((b*c - a*d)^3*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(10/3)) + ((b*c - a*d)^3*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(10/3)) - ((b*c - a*d)^3*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(10/3))","A",8,7,19,0.3684,1,"{390, 200, 31, 634, 617, 204, 628}"
16,1,173,0,0.1242282,"\int \frac{\left(c+d x^3\right)^2}{a+b x^3} \, dx","Int[(c + d*x^3)^2/(a + b*x^3),x]","-\frac{(b c-a d)^2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{7/3}}+\frac{(b c-a d)^2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{7/3}}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{7/3}}+\frac{d x (2 b c-a d)}{b^2}+\frac{d^2 x^4}{4 b}","-\frac{(b c-a d)^2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{7/3}}+\frac{(b c-a d)^2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{7/3}}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{7/3}}+\frac{d x (2 b c-a d)}{b^2}+\frac{d^2 x^4}{4 b}",1,"(d*(2*b*c - a*d)*x)/b^2 + (d^2*x^4)/(4*b) - ((b*c - a*d)^2*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(7/3)) + ((b*c - a*d)^2*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(7/3)) - ((b*c - a*d)^2*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(7/3))","A",8,7,19,0.3684,1,"{390, 200, 31, 634, 617, 204, 628}"
17,1,145,0,0.0780682,"\int \frac{c+d x^3}{a+b x^3} \, dx","Int[(c + d*x^3)/(a + b*x^3),x]","-\frac{(b c-a d) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{4/3}}+\frac{(b c-a d) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{4/3}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3}}+\frac{d x}{b}","-\frac{(b c-a d) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{4/3}}+\frac{(b c-a d) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{4/3}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3}}+\frac{d x}{b}",1,"(d*x)/b - ((b*c - a*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(4/3)) + ((b*c - a*d)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(4/3)) - ((b*c - a*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(4/3))","A",7,7,17,0.4118,1,"{388, 200, 31, 634, 617, 204, 628}"
18,1,288,0,0.1467217,"\int \frac{1}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)*(c + d*x^3)),x]","-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} (b c-a d)}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} (b c-a d)}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} (b c-a d)}+\frac{d^{2/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} (b c-a d)}-\frac{d^{2/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} (b c-a d)}+\frac{d^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} (b c-a d)}","-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} (b c-a d)}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} (b c-a d)}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} (b c-a d)}+\frac{d^{2/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} (b c-a d)}-\frac{d^{2/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} (b c-a d)}+\frac{d^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} (b c-a d)}",1,"-((b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*(b*c - a*d))) + (d^(2/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*(b*c - a*d)) + (b^(2/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*(b*c - a*d)) - (d^(2/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(2/3)*(b*c - a*d)) - (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*(b*c - a*d)) + (d^(2/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(2/3)*(b*c - a*d))","A",13,7,19,0.3684,1,"{391, 200, 31, 634, 617, 204, 628}"
19,1,346,0,0.2700034,"\int \frac{1}{\left(a+b x^3\right) \left(c+d x^3\right)^2} \, dx","Int[1/((a + b*x^3)*(c + d*x^3)^2),x]","-\frac{b^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} (b c-a d)^2}+\frac{b^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} (b c-a d)^2}-\frac{b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} (b c-a d)^2}+\frac{d^{2/3} (5 b c-2 a d) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{18 c^{5/3} (b c-a d)^2}-\frac{d^{2/3} (5 b c-2 a d) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{9 c^{5/3} (b c-a d)^2}+\frac{d^{2/3} (5 b c-2 a d) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} (b c-a d)^2}-\frac{d x}{3 c \left(c+d x^3\right) (b c-a d)}","-\frac{b^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} (b c-a d)^2}+\frac{b^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} (b c-a d)^2}-\frac{b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} (b c-a d)^2}+\frac{d^{2/3} (5 b c-2 a d) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{18 c^{5/3} (b c-a d)^2}-\frac{d^{2/3} (5 b c-2 a d) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{9 c^{5/3} (b c-a d)^2}+\frac{d^{2/3} (5 b c-2 a d) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} (b c-a d)^2}-\frac{d x}{3 c \left(c+d x^3\right) (b c-a d)}",1,"-(d*x)/(3*c*(b*c - a*d)*(c + d*x^3)) - (b^(5/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*(b*c - a*d)^2) + (d^(2/3)*(5*b*c - 2*a*d)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(3*Sqrt[3]*c^(5/3)*(b*c - a*d)^2) + (b^(5/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*(b*c - a*d)^2) - (d^(2/3)*(5*b*c - 2*a*d)*Log[c^(1/3) + d^(1/3)*x])/(9*c^(5/3)*(b*c - a*d)^2) - (b^(5/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*(b*c - a*d)^2) + (d^(2/3)*(5*b*c - 2*a*d)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(18*c^(5/3)*(b*c - a*d)^2)","A",14,8,19,0.4211,1,"{414, 522, 200, 31, 634, 617, 204, 628}"
20,1,320,0,0.298205,"\int \frac{\left(c+d x^3\right)^5}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^5/(a + b*x^3)^2,x]","\frac{d^3 x^4 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right)}{4 b^4}+\frac{d^2 x \left(15 a^2 b c d^2-4 a^3 d^3-20 a b^2 c^2 d+10 b^3 c^3\right)}{b^5}-\frac{(b c-a d)^4 (13 a d+2 b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{16/3}}+\frac{(b c-a d)^4 (13 a d+2 b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{16/3}}-\frac{(b c-a d)^4 (13 a d+2 b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{16/3}}+\frac{d^4 x^7 (5 b c-2 a d)}{7 b^3}+\frac{x (b c-a d)^5}{3 a b^5 \left(a+b x^3\right)}+\frac{d^5 x^{10}}{10 b^2}","\frac{d^3 x^4 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right)}{4 b^4}+\frac{d^2 x \left(15 a^2 b c d^2-4 a^3 d^3-20 a b^2 c^2 d+10 b^3 c^3\right)}{b^5}-\frac{(b c-a d)^4 (13 a d+2 b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{16/3}}+\frac{(b c-a d)^4 (13 a d+2 b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{16/3}}-\frac{(b c-a d)^4 (13 a d+2 b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{16/3}}+\frac{d^4 x^7 (5 b c-2 a d)}{7 b^3}+\frac{x (b c-a d)^5}{3 a b^5 \left(a+b x^3\right)}+\frac{d^5 x^{10}}{10 b^2}",1,"(d^2*(10*b^3*c^3 - 20*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3)*x)/b^5 + (d^3*(10*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^4)/(4*b^4) + (d^4*(5*b*c - 2*a*d)*x^7)/(7*b^3) + (d^5*x^10)/(10*b^2) + ((b*c - a*d)^5*x)/(3*a*b^5*(a + b*x^3)) - ((b*c - a*d)^4*(2*b*c + 13*a*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(16/3)) + ((b*c - a*d)^4*(2*b*c + 13*a*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(16/3)) - ((b*c - a*d)^4*(2*b*c + 13*a*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(16/3))","A",9,8,19,0.4211,1,"{390, 385, 200, 31, 634, 617, 204, 628}"
21,1,267,0,0.2264583,"\int \frac{\left(c+d x^3\right)^4}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^4/(a + b*x^3)^2,x]","\frac{d^2 x \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right)}{b^4}-\frac{(b c-a d)^3 (5 a d+b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{5/3} b^{13/3}}+\frac{2 (b c-a d)^3 (5 a d+b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{13/3}}-\frac{2 (b c-a d)^3 (5 a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{13/3}}+\frac{d^3 x^4 (2 b c-a d)}{2 b^3}+\frac{x (b c-a d)^4}{3 a b^4 \left(a+b x^3\right)}+\frac{d^4 x^7}{7 b^2}","\frac{d^2 x \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right)}{b^4}-\frac{(b c-a d)^3 (5 a d+b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{5/3} b^{13/3}}+\frac{2 (b c-a d)^3 (5 a d+b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{13/3}}-\frac{2 (b c-a d)^3 (5 a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{13/3}}+\frac{d^3 x^4 (2 b c-a d)}{2 b^3}+\frac{x (b c-a d)^4}{3 a b^4 \left(a+b x^3\right)}+\frac{d^4 x^7}{7 b^2}",1,"(d^2*(6*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*x)/b^4 + (d^3*(2*b*c - a*d)*x^4)/(2*b^3) + (d^4*x^7)/(7*b^2) + ((b*c - a*d)^4*x)/(3*a*b^4*(a + b*x^3)) - (2*(b*c - a*d)^3*(b*c + 5*a*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(13/3)) + (2*(b*c - a*d)^3*(b*c + 5*a*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(13/3)) - ((b*c - a*d)^3*(b*c + 5*a*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(9*a^(5/3)*b^(13/3))","A",9,8,19,0.4211,1,"{390, 385, 200, 31, 634, 617, 204, 628}"
22,1,234,0,0.2196661,"\int \frac{\left(c+d x^3\right)^3}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^3/(a + b*x^3)^2,x]","-\frac{(b c-a d)^2 (7 a d+2 b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{10/3}}+\frac{(b c-a d)^2 (7 a d+2 b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{10/3}}-\frac{(b c-a d)^2 (7 a d+2 b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{10/3}}+\frac{d^2 x (3 b c-2 a d)}{b^3}+\frac{x (b c-a d)^3}{3 a b^3 \left(a+b x^3\right)}+\frac{d^3 x^4}{4 b^2}","-\frac{(b c-a d)^2 (7 a d+2 b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{10/3}}+\frac{(b c-a d)^2 (7 a d+2 b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{10/3}}-\frac{(b c-a d)^2 (7 a d+2 b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{10/3}}+\frac{d^2 x (3 b c-2 a d)}{b^3}+\frac{x (b c-a d)^3}{3 a b^3 \left(a+b x^3\right)}+\frac{d^3 x^4}{4 b^2}",1,"(d^2*(3*b*c - 2*a*d)*x)/b^3 + (d^3*x^4)/(4*b^2) + ((b*c - a*d)^3*x)/(3*a*b^3*(a + b*x^3)) - ((b*c - a*d)^2*(2*b*c + 7*a*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(10/3)) + ((b*c - a*d)^2*(2*b*c + 7*a*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(10/3)) - ((b*c - a*d)^2*(2*b*c + 7*a*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(10/3))","A",9,8,19,0.4211,1,"{390, 385, 200, 31, 634, 617, 204, 628}"
23,1,203,0,0.2310956,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^2,x]","-\frac{(b c-a d) (2 a d+b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{5/3} b^{7/3}}+\frac{2 (b c-a d) (2 a d+b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{7/3}}-\frac{2 (b c-a d) (2 a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{7/3}}+\frac{x (b c-a d)^2}{3 a b^2 \left(a+b x^3\right)}+\frac{d^2 x}{b^2}","-\frac{(b c-a d) (2 a d+b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{5/3} b^{7/3}}+\frac{2 (b c-a d) (2 a d+b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{7/3}}-\frac{2 (b c-a d) (2 a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{7/3}}+\frac{x (b c-a d)^2}{3 a b^2 \left(a+b x^3\right)}+\frac{d^2 x}{b^2}",1,"(d^2*x)/b^2 + ((b*c - a*d)^2*x)/(3*a*b^2*(a + b*x^3)) - (2*(b*c - a*d)*(b*c + 2*a*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(7/3)) + (2*(b*c - a*d)*(b*c + 2*a*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(7/3)) - ((b*c - a*d)*(b*c + 2*a*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(9*a^(5/3)*b^(7/3))","A",9,8,19,0.4211,1,"{390, 385, 200, 31, 634, 617, 204, 628}"
24,1,169,0,0.0842995,"\int \frac{c+d x^3}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)/(a + b*x^3)^2,x]","-\frac{(a d+2 b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{4/3}}+\frac{(a d+2 b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{4/3}}-\frac{(a d+2 b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{4/3}}+\frac{x (b c-a d)}{3 a b \left(a+b x^3\right)}","-\frac{(a d+2 b c) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{4/3}}+\frac{(a d+2 b c) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{4/3}}-\frac{(a d+2 b c) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{4/3}}+\frac{x (b c-a d)}{3 a b \left(a+b x^3\right)}",1,"((b*c - a*d)*x)/(3*a*b*(a + b*x^3)) - ((2*b*c + a*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(4/3)) + ((2*b*c + a*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(4/3)) - ((2*b*c + a*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(4/3))","A",7,7,17,0.4118,1,"{385, 200, 31, 634, 617, 204, 628}"
25,1,346,0,0.2546387,"\int \frac{1}{\left(a+b x^3\right)^2 \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^2*(c + d*x^3)),x]","-\frac{b^{2/3} (2 b c-5 a d) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} (b c-a d)^2}+\frac{b^{2/3} (2 b c-5 a d) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} (b c-a d)^2}-\frac{b^{2/3} (2 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} (b c-a d)^2}-\frac{d^{5/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} (b c-a d)^2}+\frac{d^{5/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} (b c-a d)^2}-\frac{d^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} (b c-a d)^2}+\frac{b x}{3 a \left(a+b x^3\right) (b c-a d)}","-\frac{b^{2/3} (2 b c-5 a d) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} (b c-a d)^2}+\frac{b^{2/3} (2 b c-5 a d) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} (b c-a d)^2}-\frac{b^{2/3} (2 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} (b c-a d)^2}-\frac{d^{5/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} (b c-a d)^2}+\frac{d^{5/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} (b c-a d)^2}-\frac{d^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} (b c-a d)^2}+\frac{b x}{3 a \left(a+b x^3\right) (b c-a d)}",1,"(b*x)/(3*a*(b*c - a*d)*(a + b*x^3)) - (b^(2/3)*(2*b*c - 5*a*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*(b*c - a*d)^2) - (d^(5/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*(b*c - a*d)^2) + (b^(2/3)*(2*b*c - 5*a*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*(b*c - a*d)^2) + (d^(5/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(2/3)*(b*c - a*d)^2) - (b^(2/3)*(2*b*c - 5*a*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*(b*c - a*d)^2) - (d^(5/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(2/3)*(b*c - a*d)^2)","A",14,8,19,0.4211,1,"{414, 522, 200, 31, 634, 617, 204, 628}"
26,1,419,0,0.4934581,"\int \frac{1}{\left(a+b x^3\right)^2 \left(c+d x^3\right)^2} \, dx","Int[1/((a + b*x^3)^2*(c + d*x^3)^2),x]","-\frac{b^{5/3} (b c-4 a d) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{5/3} (b c-a d)^3}+\frac{2 b^{5/3} (b c-4 a d) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} (b c-a d)^3}-\frac{2 b^{5/3} (b c-4 a d) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} (b c-a d)^3}-\frac{d^{5/3} (4 b c-a d) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{9 c^{5/3} (b c-a d)^3}+\frac{2 d^{5/3} (4 b c-a d) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{9 c^{5/3} (b c-a d)^3}-\frac{2 d^{5/3} (4 b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} (b c-a d)^3}+\frac{b x}{3 a \left(a+b x^3\right) \left(c+d x^3\right) (b c-a d)}+\frac{d x (a d+b c)}{3 a c \left(c+d x^3\right) (b c-a d)^2}","-\frac{b^{5/3} (b c-4 a d) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{5/3} (b c-a d)^3}+\frac{2 b^{5/3} (b c-4 a d) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} (b c-a d)^3}-\frac{2 b^{5/3} (b c-4 a d) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} (b c-a d)^3}-\frac{d^{5/3} (4 b c-a d) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{9 c^{5/3} (b c-a d)^3}+\frac{2 d^{5/3} (4 b c-a d) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{9 c^{5/3} (b c-a d)^3}-\frac{2 d^{5/3} (4 b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} (b c-a d)^3}+\frac{b x}{3 a \left(a+b x^3\right) \left(c+d x^3\right) (b c-a d)}+\frac{d x (a d+b c)}{3 a c \left(c+d x^3\right) (b c-a d)^2}",1,"(d*(b*c + a*d)*x)/(3*a*c*(b*c - a*d)^2*(c + d*x^3)) + (b*x)/(3*a*(b*c - a*d)*(a + b*x^3)*(c + d*x^3)) - (2*b^(5/3)*(b*c - 4*a*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*(b*c - a*d)^3) - (2*d^(5/3)*(4*b*c - a*d)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(3*Sqrt[3]*c^(5/3)*(b*c - a*d)^3) + (2*b^(5/3)*(b*c - 4*a*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*(b*c - a*d)^3) + (2*d^(5/3)*(4*b*c - a*d)*Log[c^(1/3) + d^(1/3)*x])/(9*c^(5/3)*(b*c - a*d)^3) - (b^(5/3)*(b*c - 4*a*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(9*a^(5/3)*(b*c - a*d)^3) - (d^(5/3)*(4*b*c - a*d)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(9*c^(5/3)*(b*c - a*d)^3)","A",15,9,19,0.4737,1,"{414, 527, 522, 200, 31, 634, 617, 204, 628}"
27,1,112,0,0.0322832,"\int \left(a-b x^3\right) \left(a+b x^3\right)^{2/3} \, dx","Int[(a - b*x^3)*(a + b*x^3)^(2/3),x]","-\frac{7 a^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 \sqrt[3]{b}}+\frac{7 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} \sqrt[3]{b}}+\frac{7}{18} a x \left(a+b x^3\right)^{2/3}-\frac{1}{6} x \left(a+b x^3\right)^{5/3}","-\frac{7 a^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 \sqrt[3]{b}}+\frac{7 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} \sqrt[3]{b}}+\frac{7}{18} a x \left(a+b x^3\right)^{2/3}-\frac{1}{6} x \left(a+b x^3\right)^{5/3}",1,"(7*a*x*(a + b*x^3)^(2/3))/18 - (x*(a + b*x^3)^(5/3))/6 + (7*a^2*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(1/3)) - (7*a^2*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(18*b^(1/3))","A",3,3,20,0.1500,1,"{388, 195, 239}"
28,1,91,0,0.0195956,"\int \frac{a-b x^3}{\sqrt[3]{a+b x^3}} \, dx","Int[(a - b*x^3)/(a + b*x^3)^(1/3),x]","-\frac{1}{3} x \left(a+b x^3\right)^{2/3}-\frac{2 a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 \sqrt[3]{b}}+\frac{4 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b}}","-\frac{1}{3} x \left(a+b x^3\right)^{2/3}-\frac{2 a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 \sqrt[3]{b}}+\frac{4 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b}}",1,"-(x*(a + b*x^3)^(2/3))/3 + (4*a*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(1/3)) - (2*a*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(3*b^(1/3))","A",2,2,20,0.1000,1,"{388, 239}"
29,1,85,0,0.0125869,"\int \frac{a-b x^3}{\left(a+b x^3\right)^{4/3}} \, dx","Int[(a - b*x^3)/(a + b*x^3)^(4/3),x]","\frac{2 x}{\sqrt[3]{a+b x^3}}+\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}","\frac{2 x}{\sqrt[3]{a+b x^3}}+\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"(2*x)/(a + b*x^3)^(1/3) - ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(1/3)) + Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)]/(2*b^(1/3))","A",2,2,20,0.1000,1,"{385, 239}"
30,1,47,0,0.0093022,"\int \frac{a-b x^3}{\left(a+b x^3\right)^{7/3}} \, dx","Int[(a - b*x^3)/(a + b*x^3)^(7/3),x]","\frac{3 x}{4 a \sqrt[3]{a+b x^3}}+\frac{x \left(a-b x^3\right)}{4 a \left(a+b x^3\right)^{4/3}}","\frac{3 x}{4 a \sqrt[3]{a+b x^3}}+\frac{x \left(a-b x^3\right)}{4 a \left(a+b x^3\right)^{4/3}}",1,"(x*(a - b*x^3))/(4*a*(a + b*x^3)^(4/3)) + (3*x)/(4*a*(a + b*x^3)^(1/3))","A",2,2,20,0.1000,1,"{378, 191}"
31,1,55,0,0.0131894,"\int \frac{a-b x^3}{\left(a+b x^3\right)^{10/3}} \, dx","Int[(a - b*x^3)/(a + b*x^3)^(10/3),x]","\frac{15 x}{28 a^2 \sqrt[3]{a+b x^3}}+\frac{5 x}{28 a \left(a+b x^3\right)^{4/3}}+\frac{2 x}{7 \left(a+b x^3\right)^{7/3}}","\frac{15 x}{28 a^2 \sqrt[3]{a+b x^3}}+\frac{5 x}{28 a \left(a+b x^3\right)^{4/3}}+\frac{2 x}{7 \left(a+b x^3\right)^{7/3}}",1,"(2*x)/(7*(a + b*x^3)^(7/3)) + (5*x)/(28*a*(a + b*x^3)^(4/3)) + (15*x)/(28*a^2*(a + b*x^3)^(1/3))","A",3,3,20,0.1500,1,"{385, 192, 191}"
32,1,74,0,0.0189451,"\int \frac{a-b x^3}{\left(a+b x^3\right)^{13/3}} \, dx","Int[(a - b*x^3)/(a + b*x^3)^(13/3),x]","\frac{18 x}{35 a^3 \sqrt[3]{a+b x^3}}+\frac{6 x}{35 a^2 \left(a+b x^3\right)^{4/3}}+\frac{4 x}{35 a \left(a+b x^3\right)^{7/3}}+\frac{x}{5 \left(a+b x^3\right)^{10/3}}","\frac{18 x}{35 a^3 \sqrt[3]{a+b x^3}}+\frac{6 x}{35 a^2 \left(a+b x^3\right)^{4/3}}+\frac{4 x}{35 a \left(a+b x^3\right)^{7/3}}+\frac{x}{5 \left(a+b x^3\right)^{10/3}}",1,"x/(5*(a + b*x^3)^(10/3)) + (4*x)/(35*a*(a + b*x^3)^(7/3)) + (6*x)/(35*a^2*(a + b*x^3)^(4/3)) + (18*x)/(35*a^3*(a + b*x^3)^(1/3))","A",4,3,20,0.1500,1,"{385, 192, 191}"
33,1,93,0,0.0263103,"\int \frac{a-b x^3}{\left(a+b x^3\right)^{16/3}} \, dx","Int[(a - b*x^3)/(a + b*x^3)^(16/3),x]","\frac{891 x}{1820 a^4 \sqrt[3]{a+b x^3}}+\frac{297 x}{1820 a^3 \left(a+b x^3\right)^{4/3}}+\frac{99 x}{910 a^2 \left(a+b x^3\right)^{7/3}}+\frac{11 x}{130 a \left(a+b x^3\right)^{10/3}}+\frac{2 x}{13 \left(a+b x^3\right)^{13/3}}","\frac{891 x}{1820 a^4 \sqrt[3]{a+b x^3}}+\frac{297 x}{1820 a^3 \left(a+b x^3\right)^{4/3}}+\frac{99 x}{910 a^2 \left(a+b x^3\right)^{7/3}}+\frac{11 x}{130 a \left(a+b x^3\right)^{10/3}}+\frac{2 x}{13 \left(a+b x^3\right)^{13/3}}",1,"(2*x)/(13*(a + b*x^3)^(13/3)) + (11*x)/(130*a*(a + b*x^3)^(10/3)) + (99*x)/(910*a^2*(a + b*x^3)^(7/3)) + (297*x)/(1820*a^3*(a + b*x^3)^(4/3)) + (891*x)/(1820*a^4*(a + b*x^3)^(1/3))","A",5,3,20,0.1500,1,"{385, 192, 191}"
34,1,56,0,0.0278397,"\int \frac{\left(a+b x^3\right)^{7/3}}{a-b x^3} \, dx","Int[(a + b*x^3)^(7/3)/(a - b*x^3),x]","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};1,-\frac{7}{3};\frac{4}{3};\frac{b x^3}{a},-\frac{b x^3}{a}\right)}{\sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{7 a^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 \left(a+b x^3\right)^{2/3}}-\frac{2 \sqrt[3]{2} a^{5/3} \log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 \sqrt[3]{b}}+\frac{2 \sqrt[3]{2} a^{5/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{b}}-\frac{4 \sqrt[3]{2} a^{5/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{b}}+\frac{\sqrt[3]{2} a^{5/3} \log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{3 \sqrt[3]{b}}-\frac{4 \sqrt[3]{2} a^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{2 \sqrt[3]{2} a^{5/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{7}{5} a x \sqrt[3]{a+b x^3}-\frac{1}{5} x \left(a+b x^3\right)^{4/3}",1,"(a*x*(a + b*x^3)^(1/3)*AppellF1[1/3, 1, -7/3, 4/3, (b*x^3)/a, -((b*x^3)/a)])/(1 + (b*x^3)/a)^(1/3)","C",2,2,22,0.09091,0,"{430, 429}"
35,1,55,0,0.0261809,"\int \frac{\left(a+b x^3\right)^{4/3}}{a-b x^3} \, dx","Int[(a + b*x^3)^(4/3)/(a - b*x^3),x]","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};1,-\frac{4}{3};\frac{4}{3};\frac{b x^3}{a},-\frac{b x^3}{a}\right)}{\sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\sqrt[3]{2} a^{2/3} \log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 \sqrt[3]{b}}+\frac{\sqrt[3]{2} a^{2/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{b}}-\frac{2 \sqrt[3]{2} a^{2/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{b}}+\frac{a^{2/3} \log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{3\ 2^{2/3} \sqrt[3]{b}}-\frac{2 \sqrt[3]{2} a^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{\sqrt[3]{2} a^{2/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{a x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \left(a+b x^3\right)^{2/3}}-\frac{1}{2} x \sqrt[3]{a+b x^3}",1,"(x*(a + b*x^3)^(1/3)*AppellF1[1/3, 1, -4/3, 4/3, (b*x^3)/a, -((b*x^3)/a)])/(1 + (b*x^3)/a)^(1/3)","C",2,2,22,0.09091,0,"{430, 429}"
36,1,58,0,0.0263875,"\int \frac{\sqrt[3]{a+b x^3}}{a-b x^3} \, dx","Int[(a + b*x^3)^(1/3)/(a - b*x^3),x]","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};\frac{b x^3}{a},-\frac{b x^3}{a}\right)}{a \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3\ 2^{2/3} \sqrt[3]{a} \sqrt[3]{b}}+\frac{\log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3\ 2^{2/3} \sqrt[3]{a} \sqrt[3]{b}}-\frac{\sqrt[3]{2} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{a} \sqrt[3]{b}}+\frac{\log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{6\ 2^{2/3} \sqrt[3]{a} \sqrt[3]{b}}-\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} \sqrt[3]{a} \sqrt[3]{b}}",1,"(x*(a + b*x^3)^(1/3)*AppellF1[1/3, 1, -1/3, 4/3, (b*x^3)/a, -((b*x^3)/a)])/(a*(1 + (b*x^3)/a)^(1/3))","C",2,2,22,0.09091,0,"{430, 429}"
37,1,58,0,0.0276162,"\int \frac{1}{\left(a-b x^3\right) \left(a+b x^3\right)^{2/3}} \, dx","Int[1/((a - b*x^3)*(a + b*x^3)^(2/3)),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};1,\frac{2}{3};\frac{4}{3};\frac{b x^3}{a},-\frac{b x^3}{a}\right)}{a \left(a+b x^3\right)^{2/3}}","-\frac{\log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{6\ 2^{2/3} a^{4/3} \sqrt[3]{b}}+\frac{\log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{6\ 2^{2/3} a^{4/3} \sqrt[3]{b}}-\frac{\log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3\ 2^{2/3} a^{4/3} \sqrt[3]{b}}+\frac{\log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{12\ 2^{2/3} a^{4/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a^{4/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3} a^{4/3} \sqrt[3]{b}}+\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 a \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 1, 2/3, 4/3, (b*x^3)/a, -((b*x^3)/a)])/(a*(a + b*x^3)^(2/3))","C",2,2,22,0.09091,0,"{430, 429}"
38,1,58,0,0.0287143,"\int \frac{1}{\left(a-b x^3\right) \left(a+b x^3\right)^{5/3}} \, dx","Int[1/((a - b*x^3)*(a + b*x^3)^(5/3)),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};1,\frac{5}{3};\frac{4}{3};\frac{b x^3}{a},-\frac{b x^3}{a}\right)}{a^2 \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 a^2 \left(a+b x^3\right)^{2/3}}+\frac{x}{4 a^2 \left(a+b x^3\right)^{2/3}}-\frac{\log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{12\ 2^{2/3} a^{7/3} \sqrt[3]{b}}+\frac{\log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{12\ 2^{2/3} a^{7/3} \sqrt[3]{b}}-\frac{\log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{6\ 2^{2/3} a^{7/3} \sqrt[3]{b}}+\frac{\log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{24\ 2^{2/3} a^{7/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3} a^{7/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{4\ 2^{2/3} \sqrt{3} a^{7/3} \sqrt[3]{b}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 1, 5/3, 4/3, (b*x^3)/a, -((b*x^3)/a)])/(a^2*(a + b*x^3)^(2/3))","C",2,2,22,0.09091,0,"{430, 429}"
39,1,58,0,0.026983,"\int \frac{1}{\left(a-b x^3\right) \left(a+b x^3\right)^{8/3}} \, dx","Int[1/((a - b*x^3)*(a + b*x^3)^(8/3)),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};1,\frac{8}{3};\frac{4}{3};\frac{b x^3}{a},-\frac{b x^3}{a}\right)}{a^3 \left(a+b x^3\right)^{2/3}}","\frac{9 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{20 a^3 \left(a+b x^3\right)^{2/3}}+\frac{13 x}{40 a^3 \left(a+b x^3\right)^{2/3}}+\frac{x}{10 a^2 \left(a+b x^3\right)^{5/3}}-\frac{\log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{24\ 2^{2/3} a^{10/3} \sqrt[3]{b}}+\frac{\log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{24\ 2^{2/3} a^{10/3} \sqrt[3]{b}}-\frac{\log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{12\ 2^{2/3} a^{10/3} \sqrt[3]{b}}+\frac{\log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{48\ 2^{2/3} a^{10/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{4\ 2^{2/3} \sqrt{3} a^{10/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{8\ 2^{2/3} \sqrt{3} a^{10/3} \sqrt[3]{b}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 1, 8/3, 4/3, (b*x^3)/a, -((b*x^3)/a)])/(a^3*(a + b*x^3)^(2/3))","C",2,2,22,0.09091,0,"{430, 429}"
40,1,139,0,0.0566985,"\int \left(a-b x^3\right)^2 \left(a+b x^3\right)^{2/3} \, dx","Int[(a - b*x^3)^2*(a + b*x^3)^(2/3),x]","\frac{38}{81} a^2 x \left(a+b x^3\right)^{2/3}-\frac{38 a^3 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{81 \sqrt[3]{b}}+\frac{76 a^3 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{81 \sqrt{3} \sqrt[3]{b}}-\frac{8}{27} a x \left(a+b x^3\right)^{5/3}-\frac{1}{9} x \left(a-b x^3\right) \left(a+b x^3\right)^{5/3}","\frac{38}{81} a^2 x \left(a+b x^3\right)^{2/3}-\frac{38 a^3 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{81 \sqrt[3]{b}}+\frac{76 a^3 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{81 \sqrt{3} \sqrt[3]{b}}-\frac{8}{27} a x \left(a+b x^3\right)^{5/3}-\frac{1}{9} x \left(a-b x^3\right) \left(a+b x^3\right)^{5/3}",1,"(38*a^2*x*(a + b*x^3)^(2/3))/81 - (8*a*x*(a + b*x^3)^(5/3))/27 - (x*(a - b*x^3)*(a + b*x^3)^(5/3))/9 + (76*a^3*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]*b^(1/3)) - (38*a^3*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(81*b^(1/3))","A",4,4,22,0.1818,1,"{416, 388, 195, 239}"
41,1,120,0,0.0417399,"\int \frac{\left(a-b x^3\right)^2}{\sqrt[3]{a+b x^3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(1/3),x]","-\frac{17 a^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 \sqrt[3]{b}}+\frac{17 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} \sqrt[3]{b}}-\frac{13}{18} a x \left(a+b x^3\right)^{2/3}-\frac{1}{6} x \left(a-b x^3\right) \left(a+b x^3\right)^{2/3}","-\frac{17 a^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 \sqrt[3]{b}}+\frac{17 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} \sqrt[3]{b}}-\frac{13}{18} a x \left(a+b x^3\right)^{2/3}-\frac{1}{6} x \left(a-b x^3\right) \left(a+b x^3\right)^{2/3}",1,"(-13*a*x*(a + b*x^3)^(2/3))/18 - (x*(a - b*x^3)*(a + b*x^3)^(2/3))/6 + (17*a^2*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(1/3)) - (17*a^2*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(18*b^(1/3))","A",3,3,22,0.1364,1,"{416, 388, 239}"
42,1,113,0,0.0416018,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{4/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(4/3),x]","\frac{7}{3} x \left(a+b x^3\right)^{2/3}+\frac{2 x \left(a-b x^3\right)}{\sqrt[3]{a+b x^3}}+\frac{5 a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 \sqrt[3]{b}}-\frac{10 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b}}","\frac{7}{3} x \left(a+b x^3\right)^{2/3}+\frac{2 x \left(a-b x^3\right)}{\sqrt[3]{a+b x^3}}+\frac{5 a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 \sqrt[3]{b}}-\frac{10 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b}}",1,"(2*x*(a - b*x^3))/(a + b*x^3)^(1/3) + (7*x*(a + b*x^3)^(2/3))/3 - (10*a*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(1/3)) + (5*a*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(3*b^(1/3))","A",3,3,22,0.1364,1,"{413, 388, 239}"
43,1,110,0,0.0403552,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{7/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(7/3),x]","-\frac{x}{2 \sqrt[3]{a+b x^3}}+\frac{x \left(a-b x^3\right)}{2 \left(a+b x^3\right)^{4/3}}-\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}","-\frac{x}{2 \sqrt[3]{a+b x^3}}+\frac{x \left(a-b x^3\right)}{2 \left(a+b x^3\right)^{4/3}}-\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"(x*(a - b*x^3))/(2*(a + b*x^3)^(4/3)) - x/(2*(a + b*x^3)^(1/3)) + ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(1/3)) - Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)]/(2*b^(1/3))","A",3,3,22,0.1364,1,"{413, 385, 239}"
44,1,76,0,0.0212121,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{10/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(10/3),x]","\frac{x \left(a-b x^3\right)^2}{7 a \left(a+b x^3\right)^{7/3}}+\frac{3 x \left(a-b x^3\right)}{14 a \left(a+b x^3\right)^{4/3}}+\frac{9 x}{14 a \sqrt[3]{a+b x^3}}","\frac{x \left(a-b x^3\right)^2}{7 a \left(a+b x^3\right)^{7/3}}+\frac{3 x \left(a-b x^3\right)}{14 a \left(a+b x^3\right)^{4/3}}+\frac{9 x}{14 a \sqrt[3]{a+b x^3}}",1,"(x*(a - b*x^3)^2)/(7*a*(a + b*x^3)^(7/3)) + (3*x*(a - b*x^3))/(14*a*(a + b*x^3)^(4/3)) + (9*x)/(14*a*(a + b*x^3)^(1/3))","A",3,2,22,0.09091,1,"{378, 191}"
45,1,105,0,0.0353146,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{13/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(13/3),x]","\frac{x \left(a-b x^3\right)^3}{20 a^2 \left(a+b x^3\right)^{10/3}}+\frac{19 x \left(a-b x^3\right)^2}{140 a^2 \left(a+b x^3\right)^{7/3}}+\frac{57 x \left(a-b x^3\right)}{280 a^2 \left(a+b x^3\right)^{4/3}}+\frac{171 x}{280 a^2 \sqrt[3]{a+b x^3}}","\frac{x \left(a-b x^3\right)^3}{20 a^2 \left(a+b x^3\right)^{10/3}}+\frac{19 x \left(a-b x^3\right)^2}{140 a^2 \left(a+b x^3\right)^{7/3}}+\frac{57 x \left(a-b x^3\right)}{280 a^2 \left(a+b x^3\right)^{4/3}}+\frac{171 x}{280 a^2 \sqrt[3]{a+b x^3}}",1,"(x*(a - b*x^3)^3)/(20*a^2*(a + b*x^3)^(10/3)) + (19*x*(a - b*x^3)^2)/(140*a^2*(a + b*x^3)^(7/3)) + (57*x*(a - b*x^3))/(280*a^2*(a + b*x^3)^(4/3)) + (171*x)/(280*a^2*(a + b*x^3)^(1/3))","A",4,3,22,0.1364,1,"{382, 378, 191}"
46,1,98,0,0.0353347,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{16/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(16/3),x]","\frac{423 x}{910 a^3 \sqrt[3]{a+b x^3}}+\frac{141 x}{910 a^2 \left(a+b x^3\right)^{4/3}}+\frac{47 x}{455 a \left(a+b x^3\right)^{7/3}}+\frac{8 x}{65 \left(a+b x^3\right)^{10/3}}+\frac{2 x \left(a-b x^3\right)}{13 \left(a+b x^3\right)^{13/3}}","\frac{423 x}{910 a^3 \sqrt[3]{a+b x^3}}+\frac{141 x}{910 a^2 \left(a+b x^3\right)^{4/3}}+\frac{47 x}{455 a \left(a+b x^3\right)^{7/3}}+\frac{8 x}{65 \left(a+b x^3\right)^{10/3}}+\frac{2 x \left(a-b x^3\right)}{13 \left(a+b x^3\right)^{13/3}}",1,"(2*x*(a - b*x^3))/(13*(a + b*x^3)^(13/3)) + (8*x)/(65*(a + b*x^3)^(10/3)) + (47*x)/(455*a*(a + b*x^3)^(7/3)) + (141*x)/(910*a^2*(a + b*x^3)^(4/3)) + (423*x)/(910*a^3*(a + b*x^3)^(1/3))","A",5,4,22,0.1818,1,"{413, 385, 192, 191}"
47,1,117,0,0.0442149,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{19/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(19/3),x]","\frac{81 x}{182 a^4 \sqrt[3]{a+b x^3}}+\frac{27 x}{182 a^3 \left(a+b x^3\right)^{4/3}}+\frac{9 x}{91 a^2 \left(a+b x^3\right)^{7/3}}+\frac{x}{13 a \left(a+b x^3\right)^{10/3}}+\frac{11 x}{104 \left(a+b x^3\right)^{13/3}}+\frac{x \left(a-b x^3\right)}{8 \left(a+b x^3\right)^{16/3}}","\frac{81 x}{182 a^4 \sqrt[3]{a+b x^3}}+\frac{27 x}{182 a^3 \left(a+b x^3\right)^{4/3}}+\frac{9 x}{91 a^2 \left(a+b x^3\right)^{7/3}}+\frac{x}{13 a \left(a+b x^3\right)^{10/3}}+\frac{11 x}{104 \left(a+b x^3\right)^{13/3}}+\frac{x \left(a-b x^3\right)}{8 \left(a+b x^3\right)^{16/3}}",1,"(x*(a - b*x^3))/(8*(a + b*x^3)^(16/3)) + (11*x)/(104*(a + b*x^3)^(13/3)) + x/(13*a*(a + b*x^3)^(10/3)) + (9*x)/(91*a^2*(a + b*x^3)^(7/3)) + (27*x)/(182*a^3*(a + b*x^3)^(4/3)) + (81*x)/(182*a^4*(a + b*x^3)^(1/3))","A",6,4,22,0.1818,1,"{413, 385, 192, 191}"
48,1,94,0,0.033539,"\int \left(a-b x^3\right)^2 \left(a+b x^3\right)^{4/3} \, dx","Int[(a - b*x^3)^2*(a + b*x^3)^(4/3),x]","\frac{57 a^3 x \sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{4}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{44 \sqrt[3]{\frac{b x^3}{a}+1}}-\frac{9}{44} a x \left(a+b x^3\right)^{7/3}-\frac{1}{11} x \left(a-b x^3\right) \left(a+b x^3\right)^{7/3}","\frac{57 a^3 x \sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{4}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{44 \sqrt[3]{\frac{b x^3}{a}+1}}-\frac{9}{44} a x \left(a+b x^3\right)^{7/3}-\frac{1}{11} x \left(a-b x^3\right) \left(a+b x^3\right)^{7/3}",1,"(-9*a*x*(a + b*x^3)^(7/3))/44 - (x*(a - b*x^3)*(a + b*x^3)^(7/3))/11 + (57*a^3*x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-4/3, 1/3, 4/3, -((b*x^3)/a)])/(44*(1 + (b*x^3)/a)^(1/3))","A",4,4,22,0.1818,1,"{416, 388, 246, 245}"
49,1,94,0,0.0341371,"\int \left(a-b x^3\right)^2 \sqrt[3]{a+b x^3} \, dx","Int[(a - b*x^3)^2*(a + b*x^3)^(1/3),x]","\frac{3 a^2 x \sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \sqrt[3]{\frac{b x^3}{a}+1}}-\frac{3}{8} a x \left(a+b x^3\right)^{4/3}-\frac{1}{8} x \left(a-b x^3\right) \left(a+b x^3\right)^{4/3}","\frac{3 a^2 x \sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \sqrt[3]{\frac{b x^3}{a}+1}}-\frac{3}{8} a x \left(a+b x^3\right)^{4/3}-\frac{1}{8} x \left(a-b x^3\right) \left(a+b x^3\right)^{4/3}",1,"(-3*a*x*(a + b*x^3)^(4/3))/8 - (x*(a - b*x^3)*(a + b*x^3)^(4/3))/8 + (3*a^2*x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-1/3, 1/3, 4/3, -((b*x^3)/a)])/(2*(1 + (b*x^3)/a)^(1/3))","A",4,4,22,0.1818,1,"{416, 388, 246, 245}"
50,1,94,0,0.0341232,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{2/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(2/3),x]","\frac{12 a^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 \left(a+b x^3\right)^{2/3}}-\frac{6}{5} a x \sqrt[3]{a+b x^3}-\frac{1}{5} x \left(a-b x^3\right) \sqrt[3]{a+b x^3}","\frac{12 a^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 \left(a+b x^3\right)^{2/3}}-\frac{6}{5} a x \sqrt[3]{a+b x^3}-\frac{1}{5} x \left(a-b x^3\right) \sqrt[3]{a+b x^3}",1,"(-6*a*x*(a + b*x^3)^(1/3))/5 - (x*(a - b*x^3)*(a + b*x^3)^(1/3))/5 + (12*a^2*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(5*(a + b*x^3)^(2/3))","A",4,4,22,0.1818,1,"{416, 388, 246, 245}"
51,1,74,0,0.0339424,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{5/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(5/3),x]","\frac{3 b x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{4 \left(a+b x^3\right)^{2/3}}+\frac{x \left(a-b x^3\right)}{\left(a+b x^3\right)^{2/3}}","\frac{3 b x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{4 \left(a+b x^3\right)^{2/3}}+\frac{x \left(a-b x^3\right)}{\left(a+b x^3\right)^{2/3}}",1,"(x*(a - b*x^3))/(a + b*x^3)^(2/3) + (3*b*x^4*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[2/3, 4/3, 7/3, -((b*x^3)/a)])/(4*(a + b*x^3)^(2/3))","A",4,4,22,0.1818,1,"{413, 12, 365, 364}"
52,1,74,0,0.0269495,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{8/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(8/3),x]","\frac{3 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 \left(a+b x^3\right)^{2/3}}+\frac{2 x \left(a-b x^3\right)}{5 \left(a+b x^3\right)^{5/3}}","\frac{3 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 \left(a+b x^3\right)^{2/3}}+\frac{2 x \left(a-b x^3\right)}{5 \left(a+b x^3\right)^{5/3}}",1,"(2*x*(a - b*x^3))/(5*(a + b*x^3)^(5/3)) + (3*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(5*(a + b*x^3)^(2/3))","A",4,4,22,0.1818,1,"{413, 21, 246, 245}"
53,1,77,0,0.0257816,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{11/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(11/3),x]","\frac{3 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{8}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{4 a \left(a+b x^3\right)^{2/3}}+\frac{x \left(a-b x^3\right)}{4 \left(a+b x^3\right)^{8/3}}","\frac{3 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{8}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{4 a \left(a+b x^3\right)^{2/3}}+\frac{x \left(a-b x^3\right)}{4 \left(a+b x^3\right)^{8/3}}",1,"(x*(a - b*x^3))/(4*(a + b*x^3)^(8/3)) + (3*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 8/3, 4/3, -((b*x^3)/a)])/(4*a*(a + b*x^3)^(2/3))","A",4,4,22,0.1818,1,"{413, 12, 246, 245}"
54,1,93,0,0.033415,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{14/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(14/3),x]","\frac{15 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{8}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{22 a^2 \left(a+b x^3\right)^{2/3}}+\frac{3 x}{22 \left(a+b x^3\right)^{8/3}}+\frac{2 x \left(a-b x^3\right)}{11 \left(a+b x^3\right)^{11/3}}","\frac{15 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{8}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{22 a^2 \left(a+b x^3\right)^{2/3}}+\frac{3 x}{22 \left(a+b x^3\right)^{8/3}}+\frac{2 x \left(a-b x^3\right)}{11 \left(a+b x^3\right)^{11/3}}",1,"(2*x*(a - b*x^3))/(11*(a + b*x^3)^(11/3)) + (3*x)/(22*(a + b*x^3)^(8/3)) + (15*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 8/3, 4/3, -((b*x^3)/a)])/(22*a^2*(a + b*x^3)^(2/3))","A",4,4,22,0.1818,1,"{413, 385, 246, 245}"
55,1,93,0,0.0341936,"\int \frac{\left(a-b x^3\right)^2}{\left(a+b x^3\right)^{17/3}} \, dx","Int[(a - b*x^3)^2/(a + b*x^3)^(17/3),x]","\frac{57 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{11}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{77 a^3 \left(a+b x^3\right)^{2/3}}+\frac{9 x}{77 \left(a+b x^3\right)^{11/3}}+\frac{x \left(a-b x^3\right)}{7 \left(a+b x^3\right)^{14/3}}","\frac{57 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{11}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{77 a^3 \left(a+b x^3\right)^{2/3}}+\frac{9 x}{77 \left(a+b x^3\right)^{11/3}}+\frac{x \left(a-b x^3\right)}{7 \left(a+b x^3\right)^{14/3}}",1,"(x*(a - b*x^3))/(7*(a + b*x^3)^(14/3)) + (9*x)/(77*(a + b*x^3)^(11/3)) + (57*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 11/3, 4/3, -((b*x^3)/a)])/(77*a^3*(a + b*x^3)^(2/3))","A",4,4,22,0.1818,1,"{413, 385, 246, 245}"
56,1,174,0,0.0592267,"\int \left(a+b x^3\right)^{5/3} \left(c+d x^3\right) \, dx","Int[(a + b*x^3)^(5/3)*(c + d*x^3),x]","-\frac{5 a^2 (9 b c-a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{162 b^{4/3}}+\frac{5 a^2 (9 b c-a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{81 \sqrt{3} b^{4/3}}+\frac{x \left(a+b x^3\right)^{5/3} (9 b c-a d)}{54 b}+\frac{5 a x \left(a+b x^3\right)^{2/3} (9 b c-a d)}{162 b}+\frac{d x \left(a+b x^3\right)^{8/3}}{9 b}","-\frac{5 a^2 (9 b c-a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{162 b^{4/3}}+\frac{5 a^2 (9 b c-a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{81 \sqrt{3} b^{4/3}}+\frac{x \left(a+b x^3\right)^{5/3} (9 b c-a d)}{54 b}+\frac{5 a x \left(a+b x^3\right)^{2/3} (9 b c-a d)}{162 b}+\frac{d x \left(a+b x^3\right)^{8/3}}{9 b}",1,"(5*a*(9*b*c - a*d)*x*(a + b*x^3)^(2/3))/(162*b) + ((9*b*c - a*d)*x*(a + b*x^3)^(5/3))/(54*b) + (d*x*(a + b*x^3)^(8/3))/(9*b) + (5*a^2*(9*b*c - a*d)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]*b^(4/3)) - (5*a^2*(9*b*c - a*d)*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(162*b^(4/3))","A",4,3,19,0.1579,1,"{388, 195, 239}"
57,1,141,0,0.0450737,"\int \left(a+b x^3\right)^{2/3} \left(c+d x^3\right) \, dx","Int[(a + b*x^3)^(2/3)*(c + d*x^3),x]","-\frac{a (6 b c-a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 b^{4/3}}+\frac{a (6 b c-a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{4/3}}+\frac{x \left(a+b x^3\right)^{2/3} (6 b c-a d)}{18 b}+\frac{d x \left(a+b x^3\right)^{5/3}}{6 b}","-\frac{a (6 b c-a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 b^{4/3}}+\frac{a (6 b c-a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{4/3}}+\frac{x \left(a+b x^3\right)^{2/3} (6 b c-a d)}{18 b}+\frac{d x \left(a+b x^3\right)^{5/3}}{6 b}",1,"((6*b*c - a*d)*x*(a + b*x^3)^(2/3))/(18*b) + (d*x*(a + b*x^3)^(5/3))/(6*b) + (a*(6*b*c - a*d)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(4/3)) - (a*(6*b*c - a*d)*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(18*b^(4/3))","A",3,3,19,0.1579,1,"{388, 195, 239}"
58,1,111,0,0.0303546,"\int \frac{c+d x^3}{\sqrt[3]{a+b x^3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(1/3),x]","-\frac{(3 b c-a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{4/3}}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{d x \left(a+b x^3\right)^{2/3}}{3 b}","-\frac{(3 b c-a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{4/3}}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{d x \left(a+b x^3\right)^{2/3}}{3 b}",1,"(d*x*(a + b*x^3)^(2/3))/(3*b) + ((3*b*c - a*d)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(4/3)) - ((3*b*c - a*d)*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(6*b^(4/3))","A",2,2,19,0.1053,1,"{388, 239}"
59,1,99,0,0.0235665,"\int \frac{c+d x^3}{\left(a+b x^3\right)^{4/3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(4/3),x]","-\frac{d \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 b^{4/3}}+\frac{d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3}}+\frac{x (b c-a d)}{a b \sqrt[3]{a+b x^3}}","-\frac{d \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 b^{4/3}}+\frac{d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3}}+\frac{x (b c-a d)}{a b \sqrt[3]{a+b x^3}}",1,"((b*c - a*d)*x)/(a*b*(a + b*x^3)^(1/3)) + (d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(4/3)) - (d*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(2*b^(4/3))","A",2,2,19,0.1053,1,"{385, 239}"
60,1,47,0,0.0097775,"\int \frac{c+d x^3}{\left(a+b x^3\right)^{7/3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(7/3),x]","\frac{3 c x}{4 a^2 \sqrt[3]{a+b x^3}}+\frac{x \left(c+d x^3\right)}{4 a \left(a+b x^3\right)^{4/3}}","\frac{3 c x}{4 a^2 \sqrt[3]{a+b x^3}}+\frac{x \left(c+d x^3\right)}{4 a \left(a+b x^3\right)^{4/3}}",1,"(3*c*x)/(4*a^2*(a + b*x^3)^(1/3)) + (x*(c + d*x^3))/(4*a*(a + b*x^3)^(4/3))","A",2,2,19,0.1053,1,"{378, 191}"
61,1,91,0,0.0275407,"\int \frac{c+d x^3}{\left(a+b x^3\right)^{10/3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(10/3),x]","\frac{3 x (a d+6 b c)}{28 a^3 b \sqrt[3]{a+b x^3}}+\frac{x (a d+6 b c)}{28 a^2 b \left(a+b x^3\right)^{4/3}}+\frac{x (b c-a d)}{7 a b \left(a+b x^3\right)^{7/3}}","\frac{3 x (a d+6 b c)}{28 a^3 b \sqrt[3]{a+b x^3}}+\frac{x (a d+6 b c)}{28 a^2 b \left(a+b x^3\right)^{4/3}}+\frac{x (b c-a d)}{7 a b \left(a+b x^3\right)^{7/3}}",1,"((b*c - a*d)*x)/(7*a*b*(a + b*x^3)^(7/3)) + ((6*b*c + a*d)*x)/(28*a^2*b*(a + b*x^3)^(4/3)) + (3*(6*b*c + a*d)*x)/(28*a^3*b*(a + b*x^3)^(1/3))","A",3,3,19,0.1579,1,"{385, 192, 191}"
62,1,121,0,0.0352966,"\int \frac{c+d x^3}{\left(a+b x^3\right)^{13/3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(13/3),x]","\frac{9 x (a d+9 b c)}{140 a^4 b \sqrt[3]{a+b x^3}}+\frac{3 x (a d+9 b c)}{140 a^3 b \left(a+b x^3\right)^{4/3}}+\frac{x (a d+9 b c)}{70 a^2 b \left(a+b x^3\right)^{7/3}}+\frac{x (b c-a d)}{10 a b \left(a+b x^3\right)^{10/3}}","\frac{9 x (a d+9 b c)}{140 a^4 b \sqrt[3]{a+b x^3}}+\frac{3 x (a d+9 b c)}{140 a^3 b \left(a+b x^3\right)^{4/3}}+\frac{x (a d+9 b c)}{70 a^2 b \left(a+b x^3\right)^{7/3}}+\frac{x (b c-a d)}{10 a b \left(a+b x^3\right)^{10/3}}",1,"((b*c - a*d)*x)/(10*a*b*(a + b*x^3)^(10/3)) + ((9*b*c + a*d)*x)/(70*a^2*b*(a + b*x^3)^(7/3)) + (3*(9*b*c + a*d)*x)/(140*a^3*b*(a + b*x^3)^(4/3)) + (9*(9*b*c + a*d)*x)/(140*a^4*b*(a + b*x^3)^(1/3))","A",4,3,19,0.1579,1,"{385, 192, 191}"
63,1,151,0,0.0469943,"\int \frac{c+d x^3}{\left(a+b x^3\right)^{16/3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(16/3),x]","\frac{81 x (a d+12 b c)}{1820 a^5 b \sqrt[3]{a+b x^3}}+\frac{27 x (a d+12 b c)}{1820 a^4 b \left(a+b x^3\right)^{4/3}}+\frac{9 x (a d+12 b c)}{910 a^3 b \left(a+b x^3\right)^{7/3}}+\frac{x (a d+12 b c)}{130 a^2 b \left(a+b x^3\right)^{10/3}}+\frac{x (b c-a d)}{13 a b \left(a+b x^3\right)^{13/3}}","\frac{81 x (a d+12 b c)}{1820 a^5 b \sqrt[3]{a+b x^3}}+\frac{27 x (a d+12 b c)}{1820 a^4 b \left(a+b x^3\right)^{4/3}}+\frac{9 x (a d+12 b c)}{910 a^3 b \left(a+b x^3\right)^{7/3}}+\frac{x (a d+12 b c)}{130 a^2 b \left(a+b x^3\right)^{10/3}}+\frac{x (b c-a d)}{13 a b \left(a+b x^3\right)^{13/3}}",1,"((b*c - a*d)*x)/(13*a*b*(a + b*x^3)^(13/3)) + ((12*b*c + a*d)*x)/(130*a^2*b*(a + b*x^3)^(10/3)) + (9*(12*b*c + a*d)*x)/(910*a^3*b*(a + b*x^3)^(7/3)) + (27*(12*b*c + a*d)*x)/(1820*a^4*b*(a + b*x^3)^(4/3)) + (81*(12*b*c + a*d)*x)/(1820*a^5*b*(a + b*x^3)^(1/3))","A",5,3,19,0.1579,1,"{385, 192, 191}"
64,1,85,0,0.0228746,"\int \left(a+b x^3\right)^{7/3} \left(c+d x^3\right) \, dx","Int[(a + b*x^3)^(7/3)*(c + d*x^3),x]","\frac{a^2 x \sqrt[3]{a+b x^3} (11 b c-a d) \, _2F_1\left(-\frac{7}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{11 b \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{10/3}}{11 b}","\frac{a^2 x \sqrt[3]{a+b x^3} (11 b c-a d) \, _2F_1\left(-\frac{7}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{11 b \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{10/3}}{11 b}",1,"(d*x*(a + b*x^3)^(10/3))/(11*b) + (a^2*(11*b*c - a*d)*x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-7/3, 1/3, 4/3, -((b*x^3)/a)])/(11*b*(1 + (b*x^3)/a)^(1/3))","A",3,3,19,0.1579,1,"{388, 246, 245}"
65,1,83,0,0.0215988,"\int \left(a+b x^3\right)^{4/3} \left(c+d x^3\right) \, dx","Int[(a + b*x^3)^(4/3)*(c + d*x^3),x]","\frac{a x \sqrt[3]{a+b x^3} (8 b c-a d) \, _2F_1\left(-\frac{4}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{8 b \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{7/3}}{8 b}","\frac{a x \sqrt[3]{a+b x^3} (8 b c-a d) \, _2F_1\left(-\frac{4}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{8 b \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{7/3}}{8 b}",1,"(d*x*(a + b*x^3)^(7/3))/(8*b) + (a*(8*b*c - a*d)*x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-4/3, 1/3, 4/3, -((b*x^3)/a)])/(8*b*(1 + (b*x^3)/a)^(1/3))","A",3,3,19,0.1579,1,"{388, 246, 245}"
66,1,82,0,0.0210526,"\int \sqrt[3]{a+b x^3} \left(c+d x^3\right) \, dx","Int[(a + b*x^3)^(1/3)*(c + d*x^3),x]","\frac{x \sqrt[3]{a+b x^3} (5 b c-a d) \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 b \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{4/3}}{5 b}","\frac{x \sqrt[3]{a+b x^3} (5 b c-a d) \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 b \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{4/3}}{5 b}",1,"(d*x*(a + b*x^3)^(4/3))/(5*b) + ((5*b*c - a*d)*x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-1/3, 1/3, 4/3, -((b*x^3)/a)])/(5*b*(1 + (b*x^3)/a)^(1/3))","A",3,3,19,0.1579,1,"{388, 246, 245}"
67,1,82,0,0.0219141,"\int \frac{c+d x^3}{\left(a+b x^3\right)^{2/3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(2/3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} (2 b c-a d) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 b \left(a+b x^3\right)^{2/3}}+\frac{d x \sqrt[3]{a+b x^3}}{2 b}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} (2 b c-a d) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 b \left(a+b x^3\right)^{2/3}}+\frac{d x \sqrt[3]{a+b x^3}}{2 b}",1,"(d*x*(a + b*x^3)^(1/3))/(2*b) + ((2*b*c - a*d)*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(2*b*(a + b*x^3)^(2/3))","A",3,3,19,0.1579,1,"{388, 246, 245}"
68,1,93,0,0.0252296,"\int \frac{c+d x^3}{\left(a+b x^3\right)^{5/3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(5/3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} (a d+b c) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 a b \left(a+b x^3\right)^{2/3}}+\frac{x (b c-a d)}{2 a b \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} (a d+b c) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 a b \left(a+b x^3\right)^{2/3}}+\frac{x (b c-a d)}{2 a b \left(a+b x^3\right)^{2/3}}",1,"((b*c - a*d)*x)/(2*a*b*(a + b*x^3)^(2/3)) + ((b*c + a*d)*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(2*a*b*(a + b*x^3)^(2/3))","A",3,3,19,0.1579,1,"{385, 246, 245}"
69,1,94,0,0.02768,"\int \frac{c+d x^3}{\left(a+b x^3\right)^{8/3}} \, dx","Int[(c + d*x^3)/(a + b*x^3)^(8/3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} (a d+4 b c) \, _2F_1\left(\frac{1}{3},\frac{5}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 a^2 b \left(a+b x^3\right)^{2/3}}+\frac{x (b c-a d)}{5 a b \left(a+b x^3\right)^{5/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} (a d+4 b c) \, _2F_1\left(\frac{1}{3},\frac{5}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 a^2 b \left(a+b x^3\right)^{2/3}}+\frac{x (b c-a d)}{5 a b \left(a+b x^3\right)^{5/3}}",1,"((b*c - a*d)*x)/(5*a*b*(a + b*x^3)^(5/3)) + ((4*b*c + a*d)*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 5/3, 4/3, -((b*x^3)/a)])/(5*a^2*b*(a + b*x^3)^(2/3))","A",3,3,19,0.1579,1,"{385, 246, 245}"
70,1,262,0,0.1649219,"\int \left(a+b x^3\right)^{5/3} \left(c+d x^3\right)^2 \, dx","Int[(a + b*x^3)^(5/3)*(c + d*x^3)^2,x]","\frac{x \left(a+b x^3\right)^{5/3} \left(a^2 d^2-6 a b c d+27 b^2 c^2\right)}{162 b^2}+\frac{5 a x \left(a+b x^3\right)^{2/3} \left(a^2 d^2-6 a b c d+27 b^2 c^2\right)}{486 b^2}-\frac{5 a^2 \left(a^2 d^2-6 a b c d+27 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{486 b^{7/3}}+\frac{5 a^2 \left(a^2 d^2-6 a b c d+27 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{243 \sqrt{3} b^{7/3}}+\frac{d x \left(a+b x^3\right)^{8/3} (15 b c-4 a d)}{108 b^2}+\frac{d x \left(a+b x^3\right)^{8/3} \left(c+d x^3\right)}{12 b}","\frac{x \left(a+b x^3\right)^{5/3} \left(a^2 d^2-6 a b c d+27 b^2 c^2\right)}{162 b^2}+\frac{5 a x \left(a+b x^3\right)^{2/3} \left(a^2 d^2-6 a b c d+27 b^2 c^2\right)}{486 b^2}-\frac{5 a^2 \left(a^2 d^2-6 a b c d+27 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{486 b^{7/3}}+\frac{5 a^2 \left(a^2 d^2-6 a b c d+27 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{243 \sqrt{3} b^{7/3}}+\frac{d x \left(a+b x^3\right)^{8/3} (15 b c-4 a d)}{108 b^2}+\frac{d x \left(a+b x^3\right)^{8/3} \left(c+d x^3\right)}{12 b}",1,"(5*a*(27*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*x*(a + b*x^3)^(2/3))/(486*b^2) + ((27*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*x*(a + b*x^3)^(5/3))/(162*b^2) + (d*(15*b*c - 4*a*d)*x*(a + b*x^3)^(8/3))/(108*b^2) + (d*x*(a + b*x^3)^(8/3)*(c + d*x^3))/(12*b) + (5*a^2*(27*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(243*Sqrt[3]*b^(7/3)) - (5*a^2*(27*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(486*b^(7/3))","A",5,4,21,0.1905,1,"{416, 388, 195, 239}"
71,1,219,0,0.1663108,"\int \left(a+b x^3\right)^{2/3} \left(c+d x^3\right)^2 \, dx","Int[(a + b*x^3)^(2/3)*(c + d*x^3)^2,x]","\frac{x \left(a+b x^3\right)^{2/3} \left(2 a^2 d^2-9 a b c d+27 b^2 c^2\right)}{81 b^2}-\frac{a \left(2 a^2 d^2-9 a b c d+27 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{81 b^{7/3}}+\frac{2 a \left(2 a^2 d^2-9 a b c d+27 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{81 \sqrt{3} b^{7/3}}+\frac{2 d x \left(a+b x^3\right)^{5/3} (3 b c-a d)}{27 b^2}+\frac{d x \left(a+b x^3\right)^{5/3} \left(c+d x^3\right)}{9 b}","\frac{x \left(a+b x^3\right)^{2/3} \left(2 a^2 d^2-9 a b c d+27 b^2 c^2\right)}{81 b^2}-\frac{a \left(2 a^2 d^2-9 a b c d+27 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{81 b^{7/3}}+\frac{2 a \left(2 a^2 d^2-9 a b c d+27 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{81 \sqrt{3} b^{7/3}}+\frac{2 d x \left(a+b x^3\right)^{5/3} (3 b c-a d)}{27 b^2}+\frac{d x \left(a+b x^3\right)^{5/3} \left(c+d x^3\right)}{9 b}",1,"((27*b^2*c^2 - 9*a*b*c*d + 2*a^2*d^2)*x*(a + b*x^3)^(2/3))/(81*b^2) + (2*d*(3*b*c - a*d)*x*(a + b*x^3)^(5/3))/(27*b^2) + (d*x*(a + b*x^3)^(5/3)*(c + d*x^3))/(9*b) + (2*a*(27*b^2*c^2 - 9*a*b*c*d + 2*a^2*d^2)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]*b^(7/3)) - (a*(27*b^2*c^2 - 9*a*b*c*d + 2*a^2*d^2)*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(81*b^(7/3))","A",4,4,21,0.1905,1,"{416, 388, 195, 239}"
72,1,175,0,0.096277,"\int \frac{\left(c+d x^3\right)^2}{\sqrt[3]{a+b x^3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(1/3),x]","-\frac{\left(2 a^2 d^2-6 a b c d+9 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 b^{7/3}}+\frac{\left(2 a^2 d^2-6 a b c d+9 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{7/3}}+\frac{d x \left(a+b x^3\right)^{2/3} (9 b c-4 a d)}{18 b^2}+\frac{d x \left(a+b x^3\right)^{2/3} \left(c+d x^3\right)}{6 b}","-\frac{\left(2 a^2 d^2-6 a b c d+9 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 b^{7/3}}+\frac{\left(2 a^2 d^2-6 a b c d+9 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{7/3}}+\frac{d x \left(a+b x^3\right)^{2/3} (9 b c-4 a d)}{18 b^2}+\frac{d x \left(a+b x^3\right)^{2/3} \left(c+d x^3\right)}{6 b}",1,"(d*(9*b*c - 4*a*d)*x*(a + b*x^3)^(2/3))/(18*b^2) + (d*x*(a + b*x^3)^(2/3)*(c + d*x^3))/(6*b) + ((9*b^2*c^2 - 6*a*b*c*d + 2*a^2*d^2)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(7/3)) - ((9*b^2*c^2 - 6*a*b*c*d + 2*a^2*d^2)*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(18*b^(7/3))","A",3,3,21,0.1429,1,"{416, 388, 239}"
73,1,159,0,0.1023335,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{4/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(4/3),x]","-\frac{d x \left(a+b x^3\right)^{2/3} (3 b c-4 a d)}{3 a b^2}-\frac{d (3 b c-2 a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 b^{7/3}}+\frac{2 d (3 b c-2 a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{7/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{a b \sqrt[3]{a+b x^3}}","-\frac{d x \left(a+b x^3\right)^{2/3} (3 b c-4 a d)}{3 a b^2}-\frac{d (3 b c-2 a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 b^{7/3}}+\frac{2 d (3 b c-2 a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{7/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{a b \sqrt[3]{a+b x^3}}",1,"-(d*(3*b*c - 4*a*d)*x*(a + b*x^3)^(2/3))/(3*a*b^2) + ((b*c - a*d)*x*(c + d*x^3))/(a*b*(a + b*x^3)^(1/3)) + (2*d*(3*b*c - 2*a*d)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(7/3)) - (d*(3*b*c - 2*a*d)*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(3*b^(7/3))","A",3,3,21,0.1429,1,"{413, 388, 239}"
74,1,152,0,0.0676022,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{7/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(7/3),x]","\frac{x (b c-a d) (4 a d+3 b c)}{4 a^2 b^2 \sqrt[3]{a+b x^3}}-\frac{d^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 b^{7/3}}+\frac{d^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{7/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{4 a b \left(a+b x^3\right)^{4/3}}","\frac{x (b c-a d) (4 a d+3 b c)}{4 a^2 b^2 \sqrt[3]{a+b x^3}}-\frac{d^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 b^{7/3}}+\frac{d^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{7/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{4 a b \left(a+b x^3\right)^{4/3}}",1,"((b*c - a*d)*(3*b*c + 4*a*d)*x)/(4*a^2*b^2*(a + b*x^3)^(1/3)) + ((b*c - a*d)*x*(c + d*x^3))/(4*a*b*(a + b*x^3)^(4/3)) + (d^2*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(7/3)) - (d^2*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(2*b^(7/3))","A",3,3,21,0.1429,1,"{413, 385, 239}"
75,1,78,0,0.0211033,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{10/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(10/3),x]","\frac{9 c^2 x}{14 a^3 \sqrt[3]{a+b x^3}}+\frac{3 c x \left(c+d x^3\right)}{14 a^2 \left(a+b x^3\right)^{4/3}}+\frac{x \left(c+d x^3\right)^2}{7 a \left(a+b x^3\right)^{7/3}}","\frac{9 c^2 x}{14 a^3 \sqrt[3]{a+b x^3}}+\frac{3 c x \left(c+d x^3\right)}{14 a^2 \left(a+b x^3\right)^{4/3}}+\frac{x \left(c+d x^3\right)^2}{7 a \left(a+b x^3\right)^{7/3}}",1,"(9*c^2*x)/(14*a^3*(a + b*x^3)^(1/3)) + (3*c*x*(c + d*x^3))/(14*a^2*(a + b*x^3)^(4/3)) + (x*(c + d*x^3)^2)/(7*a*(a + b*x^3)^(7/3))","A",3,2,21,0.09524,1,"{378, 191}"
76,1,174,0,0.0726912,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{13/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(13/3),x]","\frac{9 c^2 x (9 b c-10 a d)}{140 a^4 \sqrt[3]{a+b x^3} (b c-a d)}+\frac{x \left(c+d x^3\right)^2 (9 b c-10 a d)}{70 a^2 \left(a+b x^3\right)^{7/3} (b c-a d)}+\frac{3 c x \left(c+d x^3\right) (9 b c-10 a d)}{140 a^3 \left(a+b x^3\right)^{4/3} (b c-a d)}+\frac{b x \left(c+d x^3\right)^3}{10 a \left(a+b x^3\right)^{10/3} (b c-a d)}","\frac{9 c^2 x (9 b c-10 a d)}{140 a^4 \sqrt[3]{a+b x^3} (b c-a d)}+\frac{x \left(c+d x^3\right)^2 (9 b c-10 a d)}{70 a^2 \left(a+b x^3\right)^{7/3} (b c-a d)}+\frac{3 c x \left(c+d x^3\right) (9 b c-10 a d)}{140 a^3 \left(a+b x^3\right)^{4/3} (b c-a d)}+\frac{b x \left(c+d x^3\right)^3}{10 a \left(a+b x^3\right)^{10/3} (b c-a d)}",1,"(9*c^2*(9*b*c - 10*a*d)*x)/(140*a^4*(b*c - a*d)*(a + b*x^3)^(1/3)) + (3*c*(9*b*c - 10*a*d)*x*(c + d*x^3))/(140*a^3*(b*c - a*d)*(a + b*x^3)^(4/3)) + ((9*b*c - 10*a*d)*x*(c + d*x^3)^2)/(70*a^2*(b*c - a*d)*(a + b*x^3)^(7/3)) + (b*x*(c + d*x^3)^3)/(10*a*(b*c - a*d)*(a + b*x^3)^(10/3))","A",4,3,21,0.1429,1,"{382, 378, 191}"
77,1,211,0,0.1273527,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{16/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(16/3),x]","\frac{9 x \left(2 a^2 d^2+9 a b c d+54 b^2 c^2\right)}{910 a^5 b^2 \sqrt[3]{a+b x^3}}+\frac{3 x \left(2 a^2 d^2+9 a b c d+54 b^2 c^2\right)}{910 a^4 b^2 \left(a+b x^3\right)^{4/3}}+\frac{x \left(2 a^2 d^2+9 a b c d+54 b^2 c^2\right)}{455 a^3 b^2 \left(a+b x^3\right)^{7/3}}+\frac{2 x (b c-a d) (a d+3 b c)}{65 a^2 b^2 \left(a+b x^3\right)^{10/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{13 a b \left(a+b x^3\right)^{13/3}}","\frac{9 x \left(2 a^2 d^2+9 a b c d+54 b^2 c^2\right)}{910 a^5 b^2 \sqrt[3]{a+b x^3}}+\frac{3 x \left(2 a^2 d^2+9 a b c d+54 b^2 c^2\right)}{910 a^4 b^2 \left(a+b x^3\right)^{4/3}}+\frac{x \left(2 a^2 d^2+9 a b c d+54 b^2 c^2\right)}{455 a^3 b^2 \left(a+b x^3\right)^{7/3}}+\frac{2 x (b c-a d) (a d+3 b c)}{65 a^2 b^2 \left(a+b x^3\right)^{10/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{13 a b \left(a+b x^3\right)^{13/3}}",1,"(2*(b*c - a*d)*(3*b*c + a*d)*x)/(65*a^2*b^2*(a + b*x^3)^(10/3)) + ((54*b^2*c^2 + 9*a*b*c*d + 2*a^2*d^2)*x)/(455*a^3*b^2*(a + b*x^3)^(7/3)) + (3*(54*b^2*c^2 + 9*a*b*c*d + 2*a^2*d^2)*x)/(910*a^4*b^2*(a + b*x^3)^(4/3)) + (9*(54*b^2*c^2 + 9*a*b*c*d + 2*a^2*d^2)*x)/(910*a^5*b^2*(a + b*x^3)^(1/3)) + ((b*c - a*d)*x*(c + d*x^3))/(13*a*b*(a + b*x^3)^(13/3))","A",5,4,21,0.1905,1,"{413, 385, 192, 191}"
78,1,253,0,0.2071487,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{19/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(19/3),x]","\frac{81 x \left(a^2 d^2+6 a b c d+45 b^2 c^2\right)}{7280 a^6 b^2 \sqrt[3]{a+b x^3}}+\frac{27 x \left(a^2 d^2+6 a b c d+45 b^2 c^2\right)}{7280 a^5 b^2 \left(a+b x^3\right)^{4/3}}+\frac{9 x \left(a^2 d^2+6 a b c d+45 b^2 c^2\right)}{3640 a^4 b^2 \left(a+b x^3\right)^{7/3}}+\frac{x \left(a^2 d^2+6 a b c d+45 b^2 c^2\right)}{520 a^3 b^2 \left(a+b x^3\right)^{10/3}}+\frac{x (b c-a d) (4 a d+15 b c)}{208 a^2 b^2 \left(a+b x^3\right)^{13/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{16 a b \left(a+b x^3\right)^{16/3}}","\frac{81 x \left(a^2 d^2+6 a b c d+45 b^2 c^2\right)}{7280 a^6 b^2 \sqrt[3]{a+b x^3}}+\frac{27 x \left(a^2 d^2+6 a b c d+45 b^2 c^2\right)}{7280 a^5 b^2 \left(a+b x^3\right)^{4/3}}+\frac{9 x \left(a^2 d^2+6 a b c d+45 b^2 c^2\right)}{3640 a^4 b^2 \left(a+b x^3\right)^{7/3}}+\frac{x \left(a^2 d^2+6 a b c d+45 b^2 c^2\right)}{520 a^3 b^2 \left(a+b x^3\right)^{10/3}}+\frac{x (b c-a d) (4 a d+15 b c)}{208 a^2 b^2 \left(a+b x^3\right)^{13/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{16 a b \left(a+b x^3\right)^{16/3}}",1,"((b*c - a*d)*(15*b*c + 4*a*d)*x)/(208*a^2*b^2*(a + b*x^3)^(13/3)) + ((45*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x)/(520*a^3*b^2*(a + b*x^3)^(10/3)) + (9*(45*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x)/(3640*a^4*b^2*(a + b*x^3)^(7/3)) + (27*(45*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x)/(7280*a^5*b^2*(a + b*x^3)^(4/3)) + (81*(45*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x)/(7280*a^6*b^2*(a + b*x^3)^(1/3)) + ((b*c - a*d)*x*(c + d*x^3))/(16*a*b*(a + b*x^3)^(16/3))","A",6,4,21,0.1905,1,"{413, 385, 192, 191}"
79,1,135,0,0.0666526,"\int \left(a+b x^3\right)^{7/3} \left(c+d x^3\right)^2 \, dx","Int[(a + b*x^3)^(7/3)*(c + d*x^3)^2,x]","\frac{a^2 x \sqrt[3]{a+b x^3} \left(2 a^2 d^2-14 a b c d+77 b^2 c^2\right) \, _2F_1\left(-\frac{7}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{77 b^2 \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{10/3} (17 b c-4 a d)}{154 b^2}+\frac{d x \left(a+b x^3\right)^{10/3} \left(c+d x^3\right)}{14 b}","\frac{a^2 x \sqrt[3]{a+b x^3} \left(2 a^2 d^2-14 a b c d+77 b^2 c^2\right) \, _2F_1\left(-\frac{7}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{77 b^2 \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{10/3} (17 b c-4 a d)}{154 b^2}+\frac{d x \left(a+b x^3\right)^{10/3} \left(c+d x^3\right)}{14 b}",1,"(d*(17*b*c - 4*a*d)*x*(a + b*x^3)^(10/3))/(154*b^2) + (d*x*(a + b*x^3)^(10/3)*(c + d*x^3))/(14*b) + (a^2*(77*b^2*c^2 - 14*a*b*c*d + 2*a^2*d^2)*x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-7/3, 1/3, 4/3, -((b*x^3)/a)])/(77*b^2*(1 + (b*x^3)/a)^(1/3))","A",4,4,21,0.1905,1,"{416, 388, 246, 245}"
80,1,133,0,0.0771186,"\int \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)^2 \, dx","Int[(a + b*x^3)^(4/3)*(c + d*x^3)^2,x]","\frac{a x \sqrt[3]{a+b x^3} \left(2 a^2 d^2-11 a b c d+44 b^2 c^2\right) \, _2F_1\left(-\frac{4}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{44 b^2 \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{7/3} (7 b c-2 a d)}{44 b^2}+\frac{d x \left(a+b x^3\right)^{7/3} \left(c+d x^3\right)}{11 b}","\frac{a x \sqrt[3]{a+b x^3} \left(2 a^2 d^2-11 a b c d+44 b^2 c^2\right) \, _2F_1\left(-\frac{4}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{44 b^2 \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{7/3} (7 b c-2 a d)}{44 b^2}+\frac{d x \left(a+b x^3\right)^{7/3} \left(c+d x^3\right)}{11 b}",1,"(d*(7*b*c - 2*a*d)*x*(a + b*x^3)^(7/3))/(44*b^2) + (d*x*(a + b*x^3)^(7/3)*(c + d*x^3))/(11*b) + (a*(44*b^2*c^2 - 11*a*b*c*d + 2*a^2*d^2)*x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-4/3, 1/3, 4/3, -((b*x^3)/a)])/(44*b^2*(1 + (b*x^3)/a)^(1/3))","A",4,4,21,0.1905,1,"{416, 388, 246, 245}"
81,1,131,0,0.061771,"\int \sqrt[3]{a+b x^3} \left(c+d x^3\right)^2 \, dx","Int[(a + b*x^3)^(1/3)*(c + d*x^3)^2,x]","\frac{x \sqrt[3]{a+b x^3} \left(a^2 d^2-4 a b c d+10 b^2 c^2\right) \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{10 b^2 \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{4/3} (11 b c-4 a d)}{40 b^2}+\frac{d x \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)}{8 b}","\frac{x \sqrt[3]{a+b x^3} \left(a^2 d^2-4 a b c d+10 b^2 c^2\right) \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{10 b^2 \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{d x \left(a+b x^3\right)^{4/3} (11 b c-4 a d)}{40 b^2}+\frac{d x \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)}{8 b}",1,"(d*(11*b*c - 4*a*d)*x*(a + b*x^3)^(4/3))/(40*b^2) + (d*x*(a + b*x^3)^(4/3)*(c + d*x^3))/(8*b) + ((10*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-1/3, 1/3, 4/3, -((b*x^3)/a)])/(10*b^2*(1 + (b*x^3)/a)^(1/3))","A",4,4,21,0.1905,1,"{416, 388, 246, 245}"
82,1,132,0,0.0754575,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{2/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(2/3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(2 a^2 d^2-5 a b c d+5 b^2 c^2\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 b^2 \left(a+b x^3\right)^{2/3}}+\frac{2 d x \sqrt[3]{a+b x^3} (2 b c-a d)}{5 b^2}+\frac{d x \sqrt[3]{a+b x^3} \left(c+d x^3\right)}{5 b}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(2 a^2 d^2-5 a b c d+5 b^2 c^2\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 b^2 \left(a+b x^3\right)^{2/3}}+\frac{2 d x \sqrt[3]{a+b x^3} (2 b c-a d)}{5 b^2}+\frac{d x \sqrt[3]{a+b x^3} \left(c+d x^3\right)}{5 b}",1,"(2*d*(2*b*c - a*d)*x*(a + b*x^3)^(1/3))/(5*b^2) + (d*x*(a + b*x^3)^(1/3)*(c + d*x^3))/(5*b) + ((5*b^2*c^2 - 5*a*b*c*d + 2*a^2*d^2)*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(5*b^2*(a + b*x^3)^(2/3))","A",4,4,21,0.1905,1,"{416, 388, 246, 245}"
83,1,146,0,0.0951581,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{5/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(5/3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(-2 a^2 d^2+2 a b c d+b^2 c^2\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 a b^2 \left(a+b x^3\right)^{2/3}}-\frac{d x \sqrt[3]{a+b x^3} (b c-2 a d)}{2 a b^2}+\frac{x \left(c+d x^3\right) (b c-a d)}{2 a b \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(-2 a^2 d^2+2 a b c d+b^2 c^2\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 a b^2 \left(a+b x^3\right)^{2/3}}-\frac{d x \sqrt[3]{a+b x^3} (b c-2 a d)}{2 a b^2}+\frac{x \left(c+d x^3\right) (b c-a d)}{2 a b \left(a+b x^3\right)^{2/3}}",1,"-(d*(b*c - 2*a*d)*x*(a + b*x^3)^(1/3))/(2*a*b^2) + ((b*c - a*d)*x*(c + d*x^3))/(2*a*b*(a + b*x^3)^(2/3)) + ((b^2*c^2 + 2*a*b*c*d - 2*a^2*d^2)*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(2*a*b^2*(a + b*x^3)^(2/3))","A",4,4,21,0.1905,1,"{413, 388, 246, 245}"
84,1,147,0,0.0877303,"\int \frac{\left(c+d x^3\right)^2}{\left(a+b x^3\right)^{8/3}} \, dx","Int[(c + d*x^3)^2/(a + b*x^3)^(8/3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(2 a^2 d^2+a b c d+2 b^2 c^2\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 a^2 b^2 \left(a+b x^3\right)^{2/3}}+\frac{2 x \left(\frac{c^2}{a^2}-\frac{d^2}{b^2}\right)}{5 \left(a+b x^3\right)^{2/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{5 a b \left(a+b x^3\right)^{5/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(2 a^2 d^2+a b c d+2 b^2 c^2\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 a^2 b^2 \left(a+b x^3\right)^{2/3}}+\frac{2 x \left(\frac{c^2}{a^2}-\frac{d^2}{b^2}\right)}{5 \left(a+b x^3\right)^{2/3}}+\frac{x \left(c+d x^3\right) (b c-a d)}{5 a b \left(a+b x^3\right)^{5/3}}",1,"(2*(c^2/a^2 - d^2/b^2)*x)/(5*(a + b*x^3)^(2/3)) + ((b*c - a*d)*x*(c + d*x^3))/(5*a*b*(a + b*x^3)^(5/3)) + ((2*b^2*c^2 + a*b*c*d + 2*a^2*d^2)*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(5*a^2*b^2*(a + b*x^3)^(2/3))","A",4,4,21,0.1905,1,"{413, 385, 246, 245}"
85,1,109,0,0.0357897,"\int \frac{\left(a+b x^3\right)^3}{\left(c+d x^3\right)^{13/3}} \, dx","Int[(a + b*x^3)^3/(c + d*x^3)^(13/3),x]","\frac{27 a^2 x \left(a+b x^3\right)}{140 c^3 \left(c+d x^3\right)^{4/3}}+\frac{81 a^3 x}{140 c^4 \sqrt[3]{c+d x^3}}+\frac{9 a x \left(a+b x^3\right)^2}{70 c^2 \left(c+d x^3\right)^{7/3}}+\frac{x \left(a+b x^3\right)^3}{10 c \left(c+d x^3\right)^{10/3}}","\frac{27 a^2 x \left(a+b x^3\right)}{140 c^3 \left(c+d x^3\right)^{4/3}}+\frac{81 a^3 x}{140 c^4 \sqrt[3]{c+d x^3}}+\frac{9 a x \left(a+b x^3\right)^2}{70 c^2 \left(c+d x^3\right)^{7/3}}+\frac{x \left(a+b x^3\right)^3}{10 c \left(c+d x^3\right)^{10/3}}",1,"(x*(a + b*x^3)^3)/(10*c*(c + d*x^3)^(10/3)) + (9*a*x*(a + b*x^3)^2)/(70*c^2*(c + d*x^3)^(7/3)) + (27*a^2*x*(a + b*x^3))/(140*c^3*(c + d*x^3)^(4/3)) + (81*a^3*x)/(140*c^4*(c + d*x^3)^(1/3))","A",4,2,21,0.09524,1,"{378, 191}"
86,1,62,0,0.0275217,"\int \frac{\left(a+b x^3\right)^{8/3}}{c+d x^3} \, dx","Int[(a + b*x^3)^(8/3)/(c + d*x^3),x]","\frac{a^2 x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{8}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{b^{2/3} \left(20 a^2 d^2-24 a b c d+9 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 d^3}+\frac{b^{2/3} \left(20 a^2 d^2-24 a b c d+9 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} d^3}-\frac{(b c-a d)^{8/3} \log \left(c+d x^3\right)}{6 c^{2/3} d^3}+\frac{(b c-a d)^{8/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} d^3}-\frac{(b c-a d)^{8/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} d^3}-\frac{b x \left(a+b x^3\right)^{2/3} (6 b c-11 a d)}{18 d^2}+\frac{b x \left(a+b x^3\right)^{5/3}}{6 d}",1,"(a^2*x*(a + b*x^3)^(2/3)*AppellF1[1/3, -8/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
87,1,60,0,0.027235,"\int \frac{\left(a+b x^3\right)^{5/3}}{c+d x^3} \, dx","Int[(a + b*x^3)^(5/3)/(c + d*x^3),x]","\frac{a x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{b^{2/3} (3 b c-5 a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 d^2}-\frac{b^{2/3} (3 b c-5 a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} d^2}+\frac{(b c-a d)^{5/3} \log \left(c+d x^3\right)}{6 c^{2/3} d^2}-\frac{(b c-a d)^{5/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} d^2}+\frac{(b c-a d)^{5/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} d^2}+\frac{b x \left(a+b x^3\right)^{2/3}}{3 d}",1,"(a*x*(a + b*x^3)^(2/3)*AppellF1[1/3, -5/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
88,1,59,0,0.0269623,"\int \frac{\left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(a + b*x^3)^(2/3)/(c + d*x^3),x]","\frac{x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{b^{2/3} \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 d}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d}-\frac{(b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^{2/3} d}+\frac{(b c-a d)^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} d}-\frac{(b c-a d)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} d}",1,"(x*(a + b*x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
89,1,207,0,0.1917956,"\int \frac{1}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{\log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{2/3} \sqrt[3]{b c-a d}}+\frac{\log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{2/3} \sqrt[3]{b c-a d}}+\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} \sqrt[3]{b c-a d}}","\frac{\log \left(c+d x^3\right)}{6 c^{2/3} \sqrt[3]{b c-a d}}-\frac{\log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} \sqrt[3]{b c-a d}}+\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} \sqrt[3]{b c-a d}}",1,"ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))]/(Sqrt[3]*c^(2/3)*(b*c - a*d)^(1/3)) - Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)]/(3*c^(2/3)*(b*c - a*d)^(1/3)) + Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)]/(6*c^(2/3)*(b*c - a*d)^(1/3))","A",7,7,21,0.3333,1,"{377, 200, 31, 634, 617, 204, 628}"
90,1,238,0,0.193167,"\int \frac{1}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{d \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{2/3} (b c-a d)^{4/3}}-\frac{d \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{2/3} (b c-a d)^{4/3}}-\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} (b c-a d)^{4/3}}+\frac{b x}{a \sqrt[3]{a+b x^3} (b c-a d)}","-\frac{d \log \left(c+d x^3\right)}{6 c^{2/3} (b c-a d)^{4/3}}+\frac{d \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} (b c-a d)^{4/3}}-\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} (b c-a d)^{4/3}}+\frac{b x}{a \sqrt[3]{a+b x^3} (b c-a d)}",1,"(b*x)/(a*(b*c - a*d)*(a + b*x^3)^(1/3)) - (d*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*(b*c - a*d)^(4/3)) + (d*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*c^(2/3)*(b*c - a*d)^(4/3)) - (d*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*c^(2/3)*(b*c - a*d)^(4/3))","A",8,8,21,0.3810,1,"{382, 377, 200, 31, 634, 617, 204, 628}"
91,1,621,0,2.580344,"\int \frac{1}{\left(a+b x^3\right)^{7/3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(7/3)*(c + d*x^3)),x]","-\frac{-9 c^2 x^9 (b c-a d)^3 \, _3F_2\left(2,2,\frac{10}{3};1,\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-9 d^2 x^{15} (b c-a d)^3 \, _3F_2\left(2,2,\frac{10}{3};1,\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-18 c d x^{12} (b c-a d)^3 \, _3F_2\left(2,2,\frac{10}{3};1,\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-180 c^3 d^2 x^6 \left(a+b x^3\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+45 c^2 d^2 x^9 \left(a+b x^3\right)^2 (b c-a d)+180 c^3 d^2 x^6 \left(a+b x^3\right)^3-33 c^2 x^9 (b c-a d)^3 \, _2F_1\left(2,\frac{10}{3};\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-420 c^4 d x^3 \left(a+b x^3\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-280 c^5 \left(a+b x^3\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+105 c^3 d x^6 \left(a+b x^3\right)^2 (b c-a d)+420 c^4 d x^3 \left(a+b x^3\right)^3+70 c^4 x^3 \left(a+b x^3\right)^2 (b c-a d)+280 c^5 \left(a+b x^3\right)^3-27 d^2 x^{15} (b c-a d)^3 \, _2F_1\left(2,\frac{10}{3};\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-60 c d x^{12} (b c-a d)^3 \, _2F_1\left(2,\frac{10}{3};\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{40 c^4 x^5 \left(a+b x^3\right)^{10/3} (b c-a d)^2}","\frac{b x (3 b c-7 a d)}{4 a^2 \sqrt[3]{a+b x^3} (b c-a d)^2}+\frac{d^2 \log \left(c+d x^3\right)}{6 c^{2/3} (b c-a d)^{7/3}}-\frac{d^2 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} (b c-a d)^{7/3}}+\frac{d^2 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} (b c-a d)^{7/3}}+\frac{b x}{4 a \left(a+b x^3\right)^{4/3} (b c-a d)}",1,"-(70*c^4*(b*c - a*d)*x^3*(a + b*x^3)^2 + 105*c^3*d*(b*c - a*d)*x^6*(a + b*x^3)^2 + 45*c^2*d^2*(b*c - a*d)*x^9*(a + b*x^3)^2 + 280*c^5*(a + b*x^3)^3 + 420*c^4*d*x^3*(a + b*x^3)^3 + 180*c^3*d^2*x^6*(a + b*x^3)^3 - 280*c^5*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 420*c^4*d*x^3*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 180*c^3*d^2*x^6*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 33*c^2*(b*c - a*d)^3*x^9*Hypergeometric2F1[2, 10/3, 13/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 60*c*d*(b*c - a*d)^3*x^12*Hypergeometric2F1[2, 10/3, 13/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 27*d^2*(b*c - a*d)^3*x^15*Hypergeometric2F1[2, 10/3, 13/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 9*c^2*(b*c - a*d)^3*x^9*HypergeometricPFQ[{2, 2, 10/3}, {1, 13/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 18*c*d*(b*c - a*d)^3*x^12*HypergeometricPFQ[{2, 2, 10/3}, {1, 13/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 9*d^2*(b*c - a*d)^3*x^15*HypergeometricPFQ[{2, 2, 10/3}, {1, 13/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(40*c^4*(b*c - a*d)^2*x^5*(a + b*x^3)^(10/3))","C",2,2,21,0.09524,0,"{430, 429}"
92,1,1172,0,6.6417093,"\int \frac{1}{\left(a+b x^3\right)^{10/3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(10/3)*(c + d*x^3)),x]","-\frac{-4158 d^3 (b c-a d)^4 \, _2F_1\left(2,\frac{13}{3};\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{21}-2268 d^3 (b c-a d)^4 \, _3F_2\left(2,2,\frac{13}{3};1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{21}-378 d^3 (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{13}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{21}-13608 c d^2 (b c-a d)^4 \, _2F_1\left(2,\frac{13}{3};\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-7182 c d^2 (b c-a d)^4 \, _3F_2\left(2,2,\frac{13}{3};1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-1134 c d^2 (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{13}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}+4212 c^2 d^3 (b c-a d)^2 \left(b x^3+a\right)^2 x^{15}-15246 c^2 d (b c-a d)^4 \, _2F_1\left(2,\frac{13}{3};\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-7560 c^2 d (b c-a d)^4 \, _3F_2\left(2,2,\frac{13}{3};1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-1134 c^2 d (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{13}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+7371 c^3 d^3 (b c-a d) \left(b x^3+a\right)^3 x^{12}+14040 c^3 d^2 (b c-a d)^2 \left(b x^3+a\right)^2 x^{12}-5796 c^3 (b c-a d)^4 \, _2F_1\left(2,\frac{13}{3};\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-2646 c^3 (b c-a d)^4 \, _3F_2\left(2,2,\frac{13}{3};1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-378 c^3 (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{13}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+29484 c^4 d^3 \left(b x^3+a\right)^4 x^9+24570 c^4 d^2 (b c-a d) \left(b x^3+a\right)^3 x^9+16380 c^4 d (b c-a d)^2 \left(b x^3+a\right)^2 x^9-29484 c^4 d^3 \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+98280 c^5 d^2 \left(b x^3+a\right)^4 x^6+28665 c^5 d (b c-a d) \left(b x^3+a\right)^3 x^6+7280 c^5 (b c-a d)^2 \left(b x^3+a\right)^2 x^6-98280 c^5 d^2 \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+114660 c^6 d \left(b x^3+a\right)^4 x^3+12740 c^6 (b c-a d) \left(b x^3+a\right)^3 x^3-114660 c^6 d \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+50960 c^7 \left(b x^3+a\right)^4-50960 c^7 \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{5096 c^5 (b c-a d)^3 x^8 \left(b x^3+a\right)^{13/3}}","\frac{b x \left(67 a^2 d^2-57 a b c d+18 b^2 c^2\right)}{28 a^3 \sqrt[3]{a+b x^3} (b c-a d)^3}+\frac{b x (6 b c-13 a d)}{28 a^2 \left(a+b x^3\right)^{4/3} (b c-a d)^2}-\frac{d^3 \log \left(c+d x^3\right)}{6 c^{2/3} (b c-a d)^{10/3}}+\frac{d^3 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} (b c-a d)^{10/3}}-\frac{d^3 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} (b c-a d)^{10/3}}+\frac{b x}{7 a \left(a+b x^3\right)^{7/3} (b c-a d)}",1,"-(7280*c^5*(b*c - a*d)^2*x^6*(a + b*x^3)^2 + 16380*c^4*d*(b*c - a*d)^2*x^9*(a + b*x^3)^2 + 14040*c^3*d^2*(b*c - a*d)^2*x^12*(a + b*x^3)^2 + 4212*c^2*d^3*(b*c - a*d)^2*x^15*(a + b*x^3)^2 + 12740*c^6*(b*c - a*d)*x^3*(a + b*x^3)^3 + 28665*c^5*d*(b*c - a*d)*x^6*(a + b*x^3)^3 + 24570*c^4*d^2*(b*c - a*d)*x^9*(a + b*x^3)^3 + 7371*c^3*d^3*(b*c - a*d)*x^12*(a + b*x^3)^3 + 50960*c^7*(a + b*x^3)^4 + 114660*c^6*d*x^3*(a + b*x^3)^4 + 98280*c^5*d^2*x^6*(a + b*x^3)^4 + 29484*c^4*d^3*x^9*(a + b*x^3)^4 - 50960*c^7*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 114660*c^6*d*x^3*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 98280*c^5*d^2*x^6*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 29484*c^4*d^3*x^9*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 5796*c^3*(b*c - a*d)^4*x^12*Hypergeometric2F1[2, 13/3, 16/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 15246*c^2*d*(b*c - a*d)^4*x^15*Hypergeometric2F1[2, 13/3, 16/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 13608*c*d^2*(b*c - a*d)^4*x^18*Hypergeometric2F1[2, 13/3, 16/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 4158*d^3*(b*c - a*d)^4*x^21*Hypergeometric2F1[2, 13/3, 16/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 2646*c^3*(b*c - a*d)^4*x^12*HypergeometricPFQ[{2, 2, 13/3}, {1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 7560*c^2*d*(b*c - a*d)^4*x^15*HypergeometricPFQ[{2, 2, 13/3}, {1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 7182*c*d^2*(b*c - a*d)^4*x^18*HypergeometricPFQ[{2, 2, 13/3}, {1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 2268*d^3*(b*c - a*d)^4*x^21*HypergeometricPFQ[{2, 2, 13/3}, {1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 378*c^3*(b*c - a*d)^4*x^12*HypergeometricPFQ[{2, 2, 2, 13/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 1134*c^2*d*(b*c - a*d)^4*x^15*HypergeometricPFQ[{2, 2, 2, 13/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 1134*c*d^2*(b*c - a*d)^4*x^18*HypergeometricPFQ[{2, 2, 2, 13/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 378*d^3*(b*c - a*d)^4*x^21*HypergeometricPFQ[{2, 2, 2, 13/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(5096*c^5*(b*c - a*d)^3*x^8*(a + b*x^3)^(13/3))","C",2,2,21,0.09524,0,"{430, 429}"
93,1,60,0,0.0283028,"\int \frac{\left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(a + b*x^3)^(4/3)/(c + d*x^3),x]","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{4}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{4}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(a*x*(a + b*x^3)^(1/3)*AppellF1[1/3, -4/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^(1/3))","A",2,2,21,0.09524,1,"{430, 429}"
94,1,59,0,0.0273635,"\int \frac{\sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(a + b*x^3)^(1/3)/(c + d*x^3),x]","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(x*(a + b*x^3)^(1/3)*AppellF1[1/3, -1/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^(1/3))","A",2,2,21,0.09524,1,"{430, 429}"
95,1,59,0,0.0275713,"\int \frac{1}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 2/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
96,1,62,0,0.0281477,"\int \frac{1}{\left(a+b x^3\right)^{5/3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(5/3)*(c + d*x^3)),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{5}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{5}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 5/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*c*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
97,1,62,0,0.0288902,"\int \frac{1}{\left(a+b x^3\right)^{8/3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(8/3)*(c + d*x^3)),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{8}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{8}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 8/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*c*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
98,1,62,0,0.0286094,"\int \frac{\left(a+b x^3\right)^{8/3}}{\left(c+d x^3\right)^2} \, dx","Int[(a + b*x^3)^(8/3)/(c + d*x^3)^2,x]","\frac{a^2 x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{8}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2 \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{b^{5/3} (3 b c-4 a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 d^3}-\frac{2 b^{5/3} (3 b c-4 a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} d^3}+\frac{(b c-a d)^{5/3} (a d+3 b c) \log \left(c+d x^3\right)}{9 c^{5/3} d^3}-\frac{(b c-a d)^{5/3} (a d+3 b c) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{3 c^{5/3} d^3}+\frac{2 (b c-a d)^{5/3} (a d+3 b c) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c^{5/3} d^3}+\frac{b x \left(a+b x^3\right)^{2/3} (2 b c-a d)}{3 c d^2}-\frac{x \left(a+b x^3\right)^{5/3} (b c-a d)}{3 c d \left(c+d x^3\right)}",1,"(a^2*x*(a + b*x^3)^(2/3)*AppellF1[1/3, -8/3, 2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^2*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
99,1,60,0,0.0279436,"\int \frac{\left(a+b x^3\right)^{5/3}}{\left(c+d x^3\right)^2} \, dx","Int[(a + b*x^3)^(5/3)/(c + d*x^3)^2,x]","\frac{a x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{5}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2 \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{b^{5/3} \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 d^2}+\frac{b^{5/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2}-\frac{(b c-a d)^{2/3} (2 a d+3 b c) \log \left(c+d x^3\right)}{18 c^{5/3} d^2}+\frac{(b c-a d)^{2/3} (2 a d+3 b c) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{6 c^{5/3} d^2}-\frac{(b c-a d)^{2/3} (2 a d+3 b c) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c^{5/3} d^2}-\frac{x \left(a+b x^3\right)^{2/3} (b c-a d)}{3 c d \left(c+d x^3\right)}",1,"(a*x*(a + b*x^3)^(2/3)*AppellF1[1/3, -5/3, 2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^2*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
100,1,241,0,0.2101149,"\int \frac{\left(a+b x^3\right)^{2/3}}{\left(c+d x^3\right)^2} \, dx","Int[(a + b*x^3)^(2/3)/(c + d*x^3)^2,x]","-\frac{2 a \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{9 c^{5/3} \sqrt[3]{b c-a d}}+\frac{a \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{9 c^{5/3} \sqrt[3]{b c-a d}}+\frac{2 a \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} \sqrt[3]{b c-a d}}+\frac{x \left(a+b x^3\right)^{2/3}}{3 c \left(c+d x^3\right)}","\frac{a \log \left(c+d x^3\right)}{9 c^{5/3} \sqrt[3]{b c-a d}}-\frac{a \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{3 c^{5/3} \sqrt[3]{b c-a d}}+\frac{2 a \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c^{5/3} \sqrt[3]{b c-a d}}+\frac{x \left(a+b x^3\right)^{2/3}}{3 c \left(c+d x^3\right)}",1,"(x*(a + b*x^3)^(2/3))/(3*c*(c + d*x^3)) + (2*a*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(3*Sqrt[3]*c^(5/3)*(b*c - a*d)^(1/3)) - (2*a*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*c^(5/3)*(b*c - a*d)^(1/3)) + (a*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*c^(5/3)*(b*c - a*d)^(1/3))","A",8,8,21,0.3810,1,"{378, 377, 200, 31, 634, 617, 204, 628}"
101,1,276,0,0.2040037,"\int \frac{1}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)^2} \, dx","Int[1/((a + b*x^3)^(1/3)*(c + d*x^3)^2),x]","-\frac{(3 b c-2 a d) \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{9 c^{5/3} (b c-a d)^{4/3}}+\frac{(3 b c-2 a d) \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{18 c^{5/3} (b c-a d)^{4/3}}+\frac{(3 b c-2 a d) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{3 \sqrt{3} c^{5/3} (b c-a d)^{4/3}}-\frac{d x \left(a+b x^3\right)^{2/3}}{3 c \left(c+d x^3\right) (b c-a d)}","\frac{(3 b c-2 a d) \log \left(c+d x^3\right)}{18 c^{5/3} (b c-a d)^{4/3}}-\frac{(3 b c-2 a d) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{6 c^{5/3} (b c-a d)^{4/3}}+\frac{(3 b c-2 a d) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c^{5/3} (b c-a d)^{4/3}}-\frac{d x \left(a+b x^3\right)^{2/3}}{3 c \left(c+d x^3\right) (b c-a d)}",1,"-(d*x*(a + b*x^3)^(2/3))/(3*c*(b*c - a*d)*(c + d*x^3)) + ((3*b*c - 2*a*d)*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(3*Sqrt[3]*c^(5/3)*(b*c - a*d)^(4/3)) - ((3*b*c - 2*a*d)*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*c^(5/3)*(b*c - a*d)^(4/3)) + ((3*b*c - 2*a*d)*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(18*c^(5/3)*(b*c - a*d)^(4/3))","A",8,8,21,0.3810,1,"{382, 377, 200, 31, 634, 617, 204, 628}"
102,1,625,0,1.9336908,"\int \frac{1}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)^2} \, dx","Int[1/((a + b*x^3)^(4/3)*(c + d*x^3)^2),x]","-\frac{c \left(a+b x^3\right)^{2/3} \left(-\frac{54 d^2 x^{15} (b c-a d)^3 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{c^5 \left(a+b x^3\right)^3}-\frac{108 d x^{12} (b c-a d)^3 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{c^4 \left(a+b x^3\right)^3}-\frac{54 x^9 (b c-a d)^3 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{13}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{c^3 \left(a+b x^3\right)^3}+\frac{2520 d^2 x^9 (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{c^3 \left(a+b x^3\right)}-\frac{6300 d^2 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{c^2}-\frac{945 d^2 x^9 (b c-a d)}{c^3 \left(a+b x^3\right)}+\frac{5320 d x^6 (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{c^2 \left(a+b x^3\right)}-\frac{1890 d x^6 (b c-a d)}{c^2 \left(a+b x^3\right)}-\frac{13720 d x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{c}+\frac{2240 x^3 (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{c \left(a+b x^3\right)}-6860 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-\frac{525 x^3 (b c-a d)}{c \left(a+b x^3\right)}+\frac{6300 d^2 x^6}{c^2}+\frac{13720 d x^3}{c}+6860\right)}{420 x^5 \left(c+d x^3\right) (b c-a d)^2}","-\frac{d (3 b c-a d) \log \left(c+d x^3\right)}{9 c^{5/3} (b c-a d)^{7/3}}+\frac{d (3 b c-a d) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{3 c^{5/3} (b c-a d)^{7/3}}-\frac{2 d (3 b c-a d) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c^{5/3} (b c-a d)^{7/3}}+\frac{b x (a d+3 b c)}{3 a c \sqrt[3]{a+b x^3} (b c-a d)^2}-\frac{d x}{3 c \sqrt[3]{a+b x^3} \left(c+d x^3\right) (b c-a d)}",1,"-(c*(a + b*x^3)^(2/3)*(6860 + (13720*d*x^3)/c + (6300*d^2*x^6)/c^2 - (525*(b*c - a*d)*x^3)/(c*(a + b*x^3)) - (1890*d*(b*c - a*d)*x^6)/(c^2*(a + b*x^3)) - (945*d^2*(b*c - a*d)*x^9)/(c^3*(a + b*x^3)) - 6860*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - (13720*d*x^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/c - (6300*d^2*x^6*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/c^2 + (2240*(b*c - a*d)*x^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(c*(a + b*x^3)) + (5320*d*(b*c - a*d)*x^6*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(c^2*(a + b*x^3)) + (2520*d^2*(b*c - a*d)*x^9*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(c^3*(a + b*x^3)) - (54*(b*c - a*d)^3*x^9*HypergeometricPFQ[{2, 2, 7/3}, {1, 13/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(c^3*(a + b*x^3)^3) - (108*d*(b*c - a*d)^3*x^12*HypergeometricPFQ[{2, 2, 7/3}, {1, 13/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(c^4*(a + b*x^3)^3) - (54*d^2*(b*c - a*d)^3*x^15*HypergeometricPFQ[{2, 2, 7/3}, {1, 13/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(c^5*(a + b*x^3)^3)))/(420*(b*c - a*d)^2*x^5*(c + d*x^3))","C",2,2,21,0.09524,0,"{430, 429}"
103,1,1214,0,5.6920996,"\int \frac{1}{\left(a+b x^3\right)^{7/3} \left(c+d x^3\right)^2} \, dx","Int[1/((a + b*x^3)^(7/3)*(c + d*x^3)^2),x]","\frac{6804 d^3 (b c-a d)^4 \, _3F_2\left(2,2,\frac{10}{3};1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{21}+1134 d^3 (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{21}+21546 c d^2 (b c-a d)^4 \, _3F_2\left(2,2,\frac{10}{3};1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}+3402 c d^2 (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}+26325 c^2 d^3 (b c-a d)^2 \left(b x^3+a\right)^2 x^{15}+22680 c^2 d (b c-a d)^4 \, _3F_2\left(2,2,\frac{10}{3};1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+3402 c^2 d (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+589680 c^3 d^3 (b c-a d) \left(b x^3+a\right)^3 x^{12}+84240 c^3 d^2 (b c-a d)^2 \left(b x^3+a\right)^2 x^{12}-966420 c^3 d^3 (b c-a d) \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+7938 c^3 (b c-a d)^4 \, _3F_2\left(2,2,\frac{10}{3};1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+1134 c^3 (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-1506960 c^4 d^3 \left(b x^3+a\right)^4 x^9+1916460 c^4 d^2 (b c-a d) \left(b x^3+a\right)^3 x^9+89505 c^4 d (b c-a d)^2 \left(b x^3+a\right)^2 x^9+1506960 c^4 d^3 \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-3144960 c^4 d^2 (b c-a d) \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-4914000 c^5 d^2 \left(b x^3+a\right)^4 x^6+2113020 c^5 d (b c-a d) \left(b x^3+a\right)^3 x^6+26130 c^5 (b c-a d)^2 \left(b x^3+a\right)^2 x^6+4914000 c^5 d^2 \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-3478020 c^5 d (b c-a d) \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-5460000 c^6 d \left(b x^3+a\right)^4 x^3+748020 c^6 (b c-a d) \left(b x^3+a\right)^3 x^3+5460000 c^6 d \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3-1248520 c^6 (b c-a d) \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3-2002000 c^7 \left(b x^3+a\right)^4+2002000 c^7 \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{21840 c^5 (b c-a d)^3 x^8 \left(b x^3+a\right)^{10/3} \left(d x^3+c\right)}","\frac{b x \left(-4 a^2 d^2-33 a b c d+9 b^2 c^2\right)}{12 a^2 c \sqrt[3]{a+b x^3} (b c-a d)^3}+\frac{d^2 (9 b c-2 a d) \log \left(c+d x^3\right)}{18 c^{5/3} (b c-a d)^{10/3}}-\frac{d^2 (9 b c-2 a d) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{6 c^{5/3} (b c-a d)^{10/3}}+\frac{d^2 (9 b c-2 a d) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c^{5/3} (b c-a d)^{10/3}}-\frac{d x}{3 c \left(a+b x^3\right)^{4/3} \left(c+d x^3\right) (b c-a d)}+\frac{b x (4 a d+3 b c)}{12 a c \left(a+b x^3\right)^{4/3} (b c-a d)^2}",1,"(26130*c^5*(b*c - a*d)^2*x^6*(a + b*x^3)^2 + 89505*c^4*d*(b*c - a*d)^2*x^9*(a + b*x^3)^2 + 84240*c^3*d^2*(b*c - a*d)^2*x^12*(a + b*x^3)^2 + 26325*c^2*d^3*(b*c - a*d)^2*x^15*(a + b*x^3)^2 + 748020*c^6*(b*c - a*d)*x^3*(a + b*x^3)^3 + 2113020*c^5*d*(b*c - a*d)*x^6*(a + b*x^3)^3 + 1916460*c^4*d^2*(b*c - a*d)*x^9*(a + b*x^3)^3 + 589680*c^3*d^3*(b*c - a*d)*x^12*(a + b*x^3)^3 - 2002000*c^7*(a + b*x^3)^4 - 5460000*c^6*d*x^3*(a + b*x^3)^4 - 4914000*c^5*d^2*x^6*(a + b*x^3)^4 - 1506960*c^4*d^3*x^9*(a + b*x^3)^4 - 1248520*c^6*(b*c - a*d)*x^3*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 3478020*c^5*d*(b*c - a*d)*x^6*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 3144960*c^4*d^2*(b*c - a*d)*x^9*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 966420*c^3*d^3*(b*c - a*d)*x^12*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 2002000*c^7*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 5460000*c^6*d*x^3*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 4914000*c^5*d^2*x^6*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1506960*c^4*d^3*x^9*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 7938*c^3*(b*c - a*d)^4*x^12*HypergeometricPFQ[{2, 2, 10/3}, {1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 22680*c^2*d*(b*c - a*d)^4*x^15*HypergeometricPFQ[{2, 2, 10/3}, {1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 21546*c*d^2*(b*c - a*d)^4*x^18*HypergeometricPFQ[{2, 2, 10/3}, {1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 6804*d^3*(b*c - a*d)^4*x^21*HypergeometricPFQ[{2, 2, 10/3}, {1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1134*c^3*(b*c - a*d)^4*x^12*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 3402*c^2*d*(b*c - a*d)^4*x^15*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 3402*c*d^2*(b*c - a*d)^4*x^18*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1134*d^3*(b*c - a*d)^4*x^21*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(21840*c^5*(b*c - a*d)^3*x^8*(a + b*x^3)^(10/3)*(c + d*x^3))","C",2,2,21,0.09524,0,"{430, 429}"
104,1,60,0,0.0272188,"\int \frac{\left(a+b x^3\right)^{4/3}}{\left(c+d x^3\right)^2} \, dx","Int[(a + b*x^3)^(4/3)/(c + d*x^3)^2,x]","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{4}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2 \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{4}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2 \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(a*x*(a + b*x^3)^(1/3)*AppellF1[1/3, -4/3, 2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^2*(1 + (b*x^3)/a)^(1/3))","A",2,2,21,0.09524,1,"{430, 429}"
105,1,59,0,0.026517,"\int \frac{\sqrt[3]{a+b x^3}}{\left(c+d x^3\right)^2} \, dx","Int[(a + b*x^3)^(1/3)/(c + d*x^3)^2,x]","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2 \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2 \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(x*(a + b*x^3)^(1/3)*AppellF1[1/3, -1/3, 2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^2*(1 + (b*x^3)/a)^(1/3))","A",2,2,21,0.09524,1,"{430, 429}"
106,1,59,0,0.0273377,"\int \frac{1}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)^2} \, dx","Int[1/((a + b*x^3)^(2/3)*(c + d*x^3)^2),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2 \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2 \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 2/3, 2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^2*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
107,1,62,0,0.0284627,"\int \frac{1}{\left(a+b x^3\right)^{5/3} \left(c+d x^3\right)^2} \, dx","Int[1/((a + b*x^3)^(5/3)*(c + d*x^3)^2),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{5}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c^2 \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{5}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c^2 \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 5/3, 2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*c^2*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
108,1,62,0,0.0278996,"\int \frac{1}{\left(a+b x^3\right)^{8/3} \left(c+d x^3\right)^2} \, dx","Int[1/((a + b*x^3)^(8/3)*(c + d*x^3)^2),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{8}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c^2 \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{8}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c^2 \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 8/3, 2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*c^2*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
109,1,62,0,0.0273345,"\int \frac{\left(a+b x^3\right)^{14/3}}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^(14/3)/(c + d*x^3)^3,x]","\frac{a^4 x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{14}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{b x \left(a+b x^3\right)^{5/3} \left(-5 a^2 d^2-10 a b c d+18 b^2 c^2\right)}{18 c^2 d^3}-\frac{b x \left(a+b x^3\right)^{2/3} (2 b c-a d) \left(-5 a^2 d^2-18 a b c d+18 b^2 c^2\right)}{18 c^2 d^4}-\frac{(b c-a d)^{8/3} \left(5 a^2 d^2+18 a b c d+54 b^2 c^2\right) \log \left(c+d x^3\right)}{54 c^{8/3} d^5}+\frac{(b c-a d)^{8/3} \left(5 a^2 d^2+18 a b c d+54 b^2 c^2\right) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{18 c^{8/3} d^5}-\frac{b^{8/3} \left(77 a^2 d^2-126 a b c d+54 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 d^5}+\frac{b^{8/3} \left(77 a^2 d^2-126 a b c d+54 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} d^5}-\frac{(b c-a d)^{8/3} \left(5 a^2 d^2+18 a b c d+54 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^{8/3} d^5}-\frac{x \left(a+b x^3\right)^{8/3} (b c-a d) (5 a d+12 b c)}{18 c^2 d^2 \left(c+d x^3\right)}-\frac{x \left(a+b x^3\right)^{11/3} (b c-a d)}{6 c d \left(c+d x^3\right)^2}",1,"(a^4*x*(a + b*x^3)^(2/3)*AppellF1[1/3, -14/3, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^3*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
110,1,62,0,0.02813,"\int \frac{\left(a+b x^3\right)^{11/3}}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^(11/3)/(c + d*x^3)^3,x]","\frac{a^3 x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{11}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{b x \left(a+b x^3\right)^{2/3} \left(-5 a^2 d^2-7 a b c d+18 b^2 c^2\right)}{18 c^2 d^3}+\frac{(b c-a d)^{5/3} \left(5 a^2 d^2+12 a b c d+27 b^2 c^2\right) \log \left(c+d x^3\right)}{54 c^{8/3} d^4}-\frac{(b c-a d)^{5/3} \left(5 a^2 d^2+12 a b c d+27 b^2 c^2\right) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{18 c^{8/3} d^4}+\frac{(b c-a d)^{5/3} \left(5 a^2 d^2+12 a b c d+27 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^{8/3} d^4}+\frac{b^{8/3} (9 b c-11 a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 d^4}-\frac{b^{8/3} (9 b c-11 a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} d^4}-\frac{x \left(a+b x^3\right)^{5/3} (b c-a d) (5 a d+9 b c)}{18 c^2 d^2 \left(c+d x^3\right)}-\frac{x \left(a+b x^3\right)^{8/3} (b c-a d)}{6 c d \left(c+d x^3\right)^2}",1,"(a^3*x*(a + b*x^3)^(2/3)*AppellF1[1/3, -11/3, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^3*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
111,1,62,0,0.0275823,"\int \frac{\left(a+b x^3\right)^{8/3}}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^(8/3)/(c + d*x^3)^3,x]","\frac{a^2 x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{8}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{(b c-a d)^{2/3} \left(5 a^2 d^2+6 a b c d+9 b^2 c^2\right) \log \left(c+d x^3\right)}{54 c^{8/3} d^3}+\frac{(b c-a d)^{2/3} \left(5 a^2 d^2+6 a b c d+9 b^2 c^2\right) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{18 c^{8/3} d^3}-\frac{(b c-a d)^{2/3} \left(5 a^2 d^2+6 a b c d+9 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^{8/3} d^3}-\frac{b^{8/3} \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 d^3}+\frac{b^{8/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^3}-\frac{x \left(a+b x^3\right)^{2/3} (b c-a d) (5 a d+6 b c)}{18 c^2 d^2 \left(c+d x^3\right)}-\frac{x \left(a+b x^3\right)^{5/3} (b c-a d)}{6 c d \left(c+d x^3\right)^2}",1,"(a^2*x*(a + b*x^3)^(2/3)*AppellF1[1/3, -8/3, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^3*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
112,1,276,0,0.2385572,"\int \frac{\left(a+b x^3\right)^{5/3}}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^(5/3)/(c + d*x^3)^3,x]","-\frac{5 a^2 \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{27 c^{8/3} \sqrt[3]{b c-a d}}+\frac{5 a^2 \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{54 c^{8/3} \sqrt[3]{b c-a d}}+\frac{5 a^2 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{9 \sqrt{3} c^{8/3} \sqrt[3]{b c-a d}}+\frac{5 a x \left(a+b x^3\right)^{2/3}}{18 c^2 \left(c+d x^3\right)}+\frac{x \left(a+b x^3\right)^{5/3}}{6 c \left(c+d x^3\right)^2}","\frac{5 a^2 \log \left(c+d x^3\right)}{54 c^{8/3} \sqrt[3]{b c-a d}}-\frac{5 a^2 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{18 c^{8/3} \sqrt[3]{b c-a d}}+\frac{5 a^2 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^{8/3} \sqrt[3]{b c-a d}}+\frac{5 a x \left(a+b x^3\right)^{2/3}}{18 c^2 \left(c+d x^3\right)}+\frac{x \left(a+b x^3\right)^{5/3}}{6 c \left(c+d x^3\right)^2}",1,"(x*(a + b*x^3)^(5/3))/(6*c*(c + d*x^3)^2) + (5*a*x*(a + b*x^3)^(2/3))/(18*c^2*(c + d*x^3)) + (5*a^2*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(9*Sqrt[3]*c^(8/3)*(b*c - a*d)^(1/3)) - (5*a^2*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(27*c^(8/3)*(b*c - a*d)^(1/3)) + (5*a^2*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(54*c^(8/3)*(b*c - a*d)^(1/3))","A",9,8,21,0.3810,1,"{378, 377, 200, 31, 634, 617, 204, 628}"
113,1,326,0,0.2434386,"\int \frac{\left(a+b x^3\right)^{2/3}}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^(2/3)/(c + d*x^3)^3,x]","\frac{x \left(a+b x^3\right)^{2/3} (6 b c-5 a d)}{18 c^2 \left(c+d x^3\right) (b c-a d)}-\frac{a (6 b c-5 a d) \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{27 c^{8/3} (b c-a d)^{4/3}}+\frac{a (6 b c-5 a d) \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{54 c^{8/3} (b c-a d)^{4/3}}+\frac{a (6 b c-5 a d) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{9 \sqrt{3} c^{8/3} (b c-a d)^{4/3}}-\frac{d x \left(a+b x^3\right)^{5/3}}{6 c \left(c+d x^3\right)^2 (b c-a d)}","\frac{x \left(a+b x^3\right)^{2/3} (6 b c-5 a d)}{18 c^2 \left(c+d x^3\right) (b c-a d)}+\frac{a (6 b c-5 a d) \log \left(c+d x^3\right)}{54 c^{8/3} (b c-a d)^{4/3}}-\frac{a (6 b c-5 a d) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{18 c^{8/3} (b c-a d)^{4/3}}+\frac{a (6 b c-5 a d) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^{8/3} (b c-a d)^{4/3}}-\frac{d x \left(a+b x^3\right)^{5/3}}{6 c \left(c+d x^3\right)^2 (b c-a d)}",1,"-(d*x*(a + b*x^3)^(5/3))/(6*c*(b*c - a*d)*(c + d*x^3)^2) + ((6*b*c - 5*a*d)*x*(a + b*x^3)^(2/3))/(18*c^2*(b*c - a*d)*(c + d*x^3)) + (a*(6*b*c - 5*a*d)*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(9*Sqrt[3]*c^(8/3)*(b*c - a*d)^(4/3)) - (a*(6*b*c - 5*a*d)*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(27*c^(8/3)*(b*c - a*d)^(4/3)) + (a*(6*b*c - 5*a*d)*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(54*c^(8/3)*(b*c - a*d)^(4/3))","A",9,9,21,0.4286,1,"{382, 378, 377, 200, 31, 634, 617, 204, 628}"
114,1,167,0,0.3101092,"\int \frac{1}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)^3} \, dx","Int[1/((a + b*x^3)^(1/3)*(c + d*x^3)^3),x]","-\frac{x \left(c d \left(-a^2 d \left(8 c+5 d x^3\right)+a b \left(12 c^2+c d x^3-5 d^2 x^6\right)+3 b^2 c x^3 \left(4 c+3 d x^3\right)\right)-2 \left(c+d x^3\right)^2 \left(5 a^2 d^2-12 a b c d+9 b^2 c^2\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)\right)}{18 c^3 \sqrt[3]{a+b x^3} \left(c+d x^3\right)^2 (b c-a d)^2}","\frac{\left(5 a^2 d^2-12 a b c d+9 b^2 c^2\right) \log \left(c+d x^3\right)}{54 c^{8/3} (b c-a d)^{7/3}}-\frac{\left(5 a^2 d^2-12 a b c d+9 b^2 c^2\right) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{18 c^{8/3} (b c-a d)^{7/3}}+\frac{\left(5 a^2 d^2-12 a b c d+9 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^{8/3} (b c-a d)^{7/3}}-\frac{d x \left(a+b x^3\right)^{2/3} (9 b c-5 a d)}{18 c^2 \left(c+d x^3\right) (b c-a d)^2}-\frac{d x \left(a+b x^3\right)^{2/3}}{6 c \left(c+d x^3\right)^2 (b c-a d)}",1,"-(x*(c*d*(3*b^2*c*x^3*(4*c + 3*d*x^3) - a^2*d*(8*c + 5*d*x^3) + a*b*(12*c^2 + c*d*x^3 - 5*d^2*x^6)) - 2*(9*b^2*c^2 - 12*a*b*c*d + 5*a^2*d^2)*(c + d*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]))/(18*c^3*(b*c - a*d)^2*(a + b*x^3)^(1/3)*(c + d*x^3)^2)","C",2,2,21,0.09524,1,"{430, 429}"
115,1,428,0,2.742305,"\int \frac{1}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)^3} \, dx","Int[1/((a + b*x^3)^(4/3)*(c + d*x^3)^3),x]","-\frac{65 c^2 \left(a+b x^3\right)^2 \left(-28 \left(c+d x^3\right)^2 \left(a^2 \left(843 c^2 d x^3+500 c^3+375 c d^2 x^6+27 d^3 x^9\right)+9 a b c x^3 \left(73 c^2+104 c d x^3+33 d^2 x^6\right)+27 b^2 c^2 x^6 \left(7 c+6 d x^3\right)\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+33657 a^2 c^2 d^3 x^9+60807 a^2 c^3 d^2 x^6+48104 a^2 c^4 d x^3+14000 a^2 c^5+7155 a^2 c d^4 x^{12}+243 a^2 d^5 x^{15}+38652 a b c^2 d^3 x^{12}+81534 a b c^3 d^2 x^9+70802 a b c^4 d x^6+21896 a b c^5 x^3+5940 a b c d^4 x^{15}+7425 b^2 c^2 d^3 x^{15}+23409 b^2 c^3 d^2 x^{12}+24417 b^2 c^4 d x^9+8391 b^2 c^5 x^6\right)-486 x^{12} \left(c+d x^3\right)^3 (b c-a d)^4 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{16}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{16380 c^5 x^8 \left(a+b x^3\right)^{7/3} \left(c+d x^3\right)^2 (b c-a d)^3}","\frac{d x \left(a+b x^3\right)^{2/3} \left(-5 a^2 d^2+15 a b c d+18 b^2 c^2\right)}{18 a c^2 \left(c+d x^3\right) (b c-a d)^3}-\frac{d \left(5 a^2 d^2-18 a b c d+27 b^2 c^2\right) \log \left(c+d x^3\right)}{54 c^{8/3} (b c-a d)^{10/3}}+\frac{d \left(5 a^2 d^2-18 a b c d+27 b^2 c^2\right) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{18 c^{8/3} (b c-a d)^{10/3}}-\frac{d \left(5 a^2 d^2-18 a b c d+27 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^{8/3} (b c-a d)^{10/3}}+\frac{b x (a d+6 b c)}{6 a c \sqrt[3]{a+b x^3} \left(c+d x^3\right) (b c-a d)^2}-\frac{d x}{6 c \sqrt[3]{a+b x^3} \left(c+d x^3\right)^2 (b c-a d)}",1,"-(65*c^2*(a + b*x^3)^2*(14000*a^2*c^5 + 21896*a*b*c^5*x^3 + 48104*a^2*c^4*d*x^3 + 8391*b^2*c^5*x^6 + 70802*a*b*c^4*d*x^6 + 60807*a^2*c^3*d^2*x^6 + 24417*b^2*c^4*d*x^9 + 81534*a*b*c^3*d^2*x^9 + 33657*a^2*c^2*d^3*x^9 + 23409*b^2*c^3*d^2*x^12 + 38652*a*b*c^2*d^3*x^12 + 7155*a^2*c*d^4*x^12 + 7425*b^2*c^2*d^3*x^15 + 5940*a*b*c*d^4*x^15 + 243*a^2*d^5*x^15 - 28*(c + d*x^3)^2*(27*b^2*c^2*x^6*(7*c + 6*d*x^3) + 9*a*b*c*x^3*(73*c^2 + 104*c*d*x^3 + 33*d^2*x^6) + a^2*(500*c^3 + 843*c^2*d*x^3 + 375*c*d^2*x^6 + 27*d^3*x^9))*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]) - 486*(b*c - a*d)^4*x^12*(c + d*x^3)^3*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 16/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(16380*c^5*(b*c - a*d)^3*x^8*(a + b*x^3)^(7/3)*(c + d*x^3)^2)","C",2,2,21,0.09524,0,"{430, 429}"
116,1,1990,0,8.6624231,"\int \frac{1}{\left(a+b x^3\right)^{7/3} \left(c+d x^3\right)^3} \, dx","Int[1/((a + b*x^3)^(7/3)*(c + d*x^3)^3),x]","-\frac{-51030 d^4 (b c-a d)^5 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{27}-5103 d^4 (b c-a d)^5 \, _5F_4\left(2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{27}-210924 c d^3 (b c-a d)^5 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{24}-20412 c d^3 (b c-a d)^5 \, _5F_4\left(2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{24}+341172 c^2 d^4 (b c-a d)^3 \left(b x^3+a\right)^2 x^{21}-326592 c^2 d^2 (b c-a d)^5 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{21}-30618 c^2 d^2 (b c-a d)^5 \, _5F_4\left(2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{21}+24261120 c^3 d^4 (b c-a d)^2 \left(b x^3+a\right)^3 x^{18}+1415232 c^3 d^3 (b c-a d)^3 \left(b x^3+a\right)^2 x^{18}-57723120 c^3 d^4 (b c-a d)^2 \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-224532 c^3 d (b c-a d)^5 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-20412 c^3 d (b c-a d)^5 \, _5F_4\left(2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-221899860 c^4 d^4 (b c-a d) \left(b x^3+a\right)^4 x^{15}+101088000 c^4 d^3 (b c-a d)^2 \left(b x^3+a\right)^3 x^{15}+2198664 c^4 d^2 (b c-a d)^3 \left(b x^3+a\right)^2 x^{15}+290384640 c^4 d^4 (b c-a d) \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-241113600 c^4 d^3 (b c-a d)^2 \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-57834 c^4 (b c-a d)^5 \, _4F_3\left(2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-5103 c^4 (b c-a d)^5 \, _5F_4\left(2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+273939120 c^5 d^4 \left(b x^3+a\right)^5 x^{12}-930252960 c^5 d^3 (b c-a d) \left(b x^3+a\right)^4 x^{12}+157697280 c^5 d^2 (b c-a d)^2 \left(b x^3+a\right)^3 x^{12}+1516320 c^5 d (b c-a d)^3 \left(b x^3+a\right)^2 x^{12}-273939120 c^5 d^4 \left(b x^3+a\right)^5 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+1218147840 c^5 d^3 (b c-a d) \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-377700960 c^5 d^2 (b c-a d)^2 \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+1151579520 c^6 d^3 \left(b x^3+a\right)^5 x^9-1466086440 c^6 d^2 (b c-a d) \left(b x^3+a\right)^4 x^9+107602560 c^6 d (b c-a d)^2 \left(b x^3+a\right)^3 x^9+522756 c^6 (b c-a d)^3 \left(b x^3+a\right)^2 x^9-1151579520 c^6 d^3 \left(b x^3+a\right)^5 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+1921920000 c^6 d^2 (b c-a d) \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-259692160 c^6 d (b c-a d)^2 \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+1823334240 c^7 d^2 \left(b x^3+a\right)^5 x^6-1019636800 c^7 d (b c-a d) \left(b x^3+a\right)^4 x^6+28042560 c^7 (b c-a d)^2 \left(b x^3+a\right)^3 x^6-1823334240 c^7 d^2 \left(b x^3+a\right)^5 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+1339520000 c^7 d (b c-a d) \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-67420080 c^7 (b c-a d)^2 \left(b x^3+a\right)^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+1279532800 c^8 d \left(b x^3+a\right)^5 x^3-265470660 c^8 (b c-a d) \left(b x^3+a\right)^4 x^3-1279532800 c^8 d \left(b x^3+a\right)^5 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+349440000 c^8 (b c-a d) \left(b x^3+a\right)^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+335877360 c^9 \left(b x^3+a\right)^5-335877360 c^9 \left(b x^3+a\right)^5 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{524160 c^6 (b c-a d)^4 x^{11} \left(b x^3+a\right)^{10/3} \left(d x^3+c\right)^2}","\frac{d x \left(a+b x^3\right)^{2/3} \left(-42 a^2 b c d^2+10 a^3 d^3-135 a b^2 c^2 d+27 b^3 c^3\right)}{36 a^2 c^2 \left(c+d x^3\right) (b c-a d)^4}+\frac{b x \left(-2 a^2 d^2-42 a b c d+9 b^2 c^2\right)}{12 a^2 c \sqrt[3]{a+b x^3} \left(c+d x^3\right) (b c-a d)^3}+\frac{d^2 \left(5 a^2 d^2-24 a b c d+54 b^2 c^2\right) \log \left(c+d x^3\right)}{54 c^{8/3} (b c-a d)^{13/3}}-\frac{d^2 \left(5 a^2 d^2-24 a b c d+54 b^2 c^2\right) \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{18 c^{8/3} (b c-a d)^{13/3}}+\frac{d^2 \left(5 a^2 d^2-24 a b c d+54 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^{8/3} (b c-a d)^{13/3}}-\frac{d x}{6 c \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)^2 (b c-a d)}+\frac{b x (2 a d+3 b c)}{12 a c \left(a+b x^3\right)^{4/3} \left(c+d x^3\right) (b c-a d)^2}",1,"-(522756*c^6*(b*c - a*d)^3*x^9*(a + b*x^3)^2 + 1516320*c^5*d*(b*c - a*d)^3*x^12*(a + b*x^3)^2 + 2198664*c^4*d^2*(b*c - a*d)^3*x^15*(a + b*x^3)^2 + 1415232*c^3*d^3*(b*c - a*d)^3*x^18*(a + b*x^3)^2 + 341172*c^2*d^4*(b*c - a*d)^3*x^21*(a + b*x^3)^2 + 28042560*c^7*(b*c - a*d)^2*x^6*(a + b*x^3)^3 + 107602560*c^6*d*(b*c - a*d)^2*x^9*(a + b*x^3)^3 + 157697280*c^5*d^2*(b*c - a*d)^2*x^12*(a + b*x^3)^3 + 101088000*c^4*d^3*(b*c - a*d)^2*x^15*(a + b*x^3)^3 + 24261120*c^3*d^4*(b*c - a*d)^2*x^18*(a + b*x^3)^3 - 265470660*c^8*(b*c - a*d)*x^3*(a + b*x^3)^4 - 1019636800*c^7*d*(b*c - a*d)*x^6*(a + b*x^3)^4 - 1466086440*c^6*d^2*(b*c - a*d)*x^9*(a + b*x^3)^4 - 930252960*c^5*d^3*(b*c - a*d)*x^12*(a + b*x^3)^4 - 221899860*c^4*d^4*(b*c - a*d)*x^15*(a + b*x^3)^4 + 335877360*c^9*(a + b*x^3)^5 + 1279532800*c^8*d*x^3*(a + b*x^3)^5 + 1823334240*c^7*d^2*x^6*(a + b*x^3)^5 + 1151579520*c^6*d^3*x^9*(a + b*x^3)^5 + 273939120*c^5*d^4*x^12*(a + b*x^3)^5 - 67420080*c^7*(b*c - a*d)^2*x^6*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 259692160*c^6*d*(b*c - a*d)^2*x^9*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 377700960*c^5*d^2*(b*c - a*d)^2*x^12*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 241113600*c^4*d^3*(b*c - a*d)^2*x^15*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 57723120*c^3*d^4*(b*c - a*d)^2*x^18*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 349440000*c^8*(b*c - a*d)*x^3*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1339520000*c^7*d*(b*c - a*d)*x^6*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1921920000*c^6*d^2*(b*c - a*d)*x^9*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1218147840*c^5*d^3*(b*c - a*d)*x^12*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 290384640*c^4*d^4*(b*c - a*d)*x^15*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 335877360*c^9*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 1279532800*c^8*d*x^3*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 1823334240*c^7*d^2*x^6*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 1151579520*c^6*d^3*x^9*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 273939120*c^5*d^4*x^12*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 57834*c^4*(b*c - a*d)^5*x^15*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 224532*c^3*d*(b*c - a*d)^5*x^18*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 326592*c^2*d^2*(b*c - a*d)^5*x^21*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 210924*c*d^3*(b*c - a*d)^5*x^24*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 51030*d^4*(b*c - a*d)^5*x^27*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 5103*c^4*(b*c - a*d)^5*x^15*HypergeometricPFQ[{2, 2, 2, 2, 10/3}, {1, 1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 20412*c^3*d*(b*c - a*d)^5*x^18*HypergeometricPFQ[{2, 2, 2, 2, 10/3}, {1, 1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 30618*c^2*d^2*(b*c - a*d)^5*x^21*HypergeometricPFQ[{2, 2, 2, 2, 10/3}, {1, 1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 20412*c*d^3*(b*c - a*d)^5*x^24*HypergeometricPFQ[{2, 2, 2, 2, 10/3}, {1, 1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 5103*d^4*(b*c - a*d)^5*x^27*HypergeometricPFQ[{2, 2, 2, 2, 10/3}, {1, 1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(524160*c^6*(b*c - a*d)^4*x^11*(a + b*x^3)^(10/3)*(c + d*x^3)^2)","C",2,2,21,0.09524,0,"{430, 429}"
117,1,60,0,0.0286702,"\int \frac{\left(a+b x^3\right)^{4/3}}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^(4/3)/(c + d*x^3)^3,x]","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{4}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{4}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(a*x*(a + b*x^3)^(1/3)*AppellF1[1/3, -4/3, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^3*(1 + (b*x^3)/a)^(1/3))","A",2,2,21,0.09524,1,"{430, 429}"
118,1,59,0,0.0259295,"\int \frac{\sqrt[3]{a+b x^3}}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^(1/3)/(c + d*x^3)^3,x]","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(x*(a + b*x^3)^(1/3)*AppellF1[1/3, -1/3, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^3*(1 + (b*x^3)/a)^(1/3))","A",2,2,21,0.09524,1,"{430, 429}"
119,1,59,0,0.0269843,"\int \frac{1}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)^3} \, dx","Int[1/((a + b*x^3)^(2/3)*(c + d*x^3)^3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3 \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 2/3, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^3*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
120,1,62,0,0.0291526,"\int \frac{1}{\left(a+b x^3\right)^{5/3} \left(c+d x^3\right)^3} \, dx","Int[1/((a + b*x^3)^(5/3)*(c + d*x^3)^3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{5}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c^3 \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{5}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c^3 \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 5/3, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*c^3*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
121,1,62,0,0.0289201,"\int \frac{1}{\left(a+b x^3\right)^{8/3} \left(c+d x^3\right)^3} \, dx","Int[1/((a + b*x^3)^(8/3)*(c + d*x^3)^3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{8}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c^3 \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{8}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c^3 \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 8/3, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*c^3*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
122,1,155,0,0.0623555,"\int \frac{\left(a+b x^3\right)^{7/4}}{\left(c+d x^3\right)^{37/12}} \, dx","Int[(a + b*x^3)^(7/4)/(c + d*x^3)^(37/12),x]","\frac{189 a^2 x \sqrt[4]{\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}} \, _2F_1\left(\frac{1}{4},\frac{1}{3};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{325 c^3 \sqrt[4]{a+b x^3} \sqrt[12]{c+d x^3}}+\frac{84 a x \left(a+b x^3\right)^{3/4}}{325 c^2 \left(c+d x^3\right)^{13/12}}+\frac{4 x \left(a+b x^3\right)^{7/4}}{25 c \left(c+d x^3\right)^{25/12}}","\frac{189 a^2 x \sqrt[4]{\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}} \, _2F_1\left(\frac{1}{4},\frac{1}{3};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{325 c^3 \sqrt[4]{a+b x^3} \sqrt[12]{c+d x^3}}+\frac{84 a x \left(a+b x^3\right)^{3/4}}{325 c^2 \left(c+d x^3\right)^{13/12}}+\frac{4 x \left(a+b x^3\right)^{7/4}}{25 c \left(c+d x^3\right)^{25/12}}",1,"(4*x*(a + b*x^3)^(7/4))/(25*c*(c + d*x^3)^(25/12)) + (84*a*x*(a + b*x^3)^(3/4))/(325*c^2*(c + d*x^3)^(13/12)) + (189*a^2*x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(1/4)*Hypergeometric2F1[1/4, 1/3, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(325*c^3*(a + b*x^3)^(1/4)*(c + d*x^3)^(1/12))","A",3,2,23,0.08696,1,"{378, 380}"
123,1,155,0,0.0577109,"\int \frac{\left(a+b x^3\right)^{5/4}}{\left(c+d x^3\right)^{31/12}} \, dx","Int[(a + b*x^3)^(5/4)/(c + d*x^3)^(31/12),x]","\frac{45 a^2 x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{133 c^3 \left(a+b x^3\right)^{3/4}}+\frac{60 a x \sqrt[4]{a+b x^3}}{133 c^2 \left(c+d x^3\right)^{7/12}}+\frac{4 x \left(a+b x^3\right)^{5/4}}{19 c \left(c+d x^3\right)^{19/12}}","\frac{45 a^2 x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{133 c^3 \left(a+b x^3\right)^{3/4}}+\frac{60 a x \sqrt[4]{a+b x^3}}{133 c^2 \left(c+d x^3\right)^{7/12}}+\frac{4 x \left(a+b x^3\right)^{5/4}}{19 c \left(c+d x^3\right)^{19/12}}",1,"(4*x*(a + b*x^3)^(5/4))/(19*c*(c + d*x^3)^(19/12)) + (60*a*x*(a + b*x^3)^(1/4))/(133*c^2*(c + d*x^3)^(7/12)) + (45*a^2*x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(3/4)*(c + d*x^3)^(5/12)*Hypergeometric2F1[1/3, 3/4, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(133*c^3*(a + b*x^3)^(3/4))","A",3,2,23,0.08696,1,"{378, 380}"
124,1,122,0,0.035532,"\int \frac{\left(a+b x^3\right)^{3/4}}{\left(c+d x^3\right)^{25/12}} \, dx","Int[(a + b*x^3)^(3/4)/(c + d*x^3)^(25/12),x]","\frac{9 a x \sqrt[4]{\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}} \, _2F_1\left(\frac{1}{4},\frac{1}{3};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{13 c^2 \sqrt[4]{a+b x^3} \sqrt[12]{c+d x^3}}+\frac{4 x \left(a+b x^3\right)^{3/4}}{13 c \left(c+d x^3\right)^{13/12}}","\frac{9 a x \sqrt[4]{\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}} \, _2F_1\left(\frac{1}{4},\frac{1}{3};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{13 c^2 \sqrt[4]{a+b x^3} \sqrt[12]{c+d x^3}}+\frac{4 x \left(a+b x^3\right)^{3/4}}{13 c \left(c+d x^3\right)^{13/12}}",1,"(4*x*(a + b*x^3)^(3/4))/(13*c*(c + d*x^3)^(13/12)) + (9*a*x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(1/4)*Hypergeometric2F1[1/4, 1/3, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(13*c^2*(a + b*x^3)^(1/4)*(c + d*x^3)^(1/12))","A",2,2,23,0.08696,1,"{378, 380}"
125,1,122,0,0.036754,"\int \frac{\sqrt[4]{a+b x^3}}{\left(c+d x^3\right)^{19/12}} \, dx","Int[(a + b*x^3)^(1/4)/(c + d*x^3)^(19/12),x]","\frac{3 a x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{7 c^2 \left(a+b x^3\right)^{3/4}}+\frac{4 x \sqrt[4]{a+b x^3}}{7 c \left(c+d x^3\right)^{7/12}}","\frac{3 a x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{7 c^2 \left(a+b x^3\right)^{3/4}}+\frac{4 x \sqrt[4]{a+b x^3}}{7 c \left(c+d x^3\right)^{7/12}}",1,"(4*x*(a + b*x^3)^(1/4))/(7*c*(c + d*x^3)^(7/12)) + (3*a*x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(3/4)*(c + d*x^3)^(5/12)*Hypergeometric2F1[1/3, 3/4, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(7*c^2*(a + b*x^3)^(3/4))","A",2,2,23,0.08696,1,"{378, 380}"
126,1,87,0,0.0168134,"\int \frac{1}{\sqrt[4]{a+b x^3} \left(c+d x^3\right)^{13/12}} \, dx","Int[1/((a + b*x^3)^(1/4)*(c + d*x^3)^(13/12)),x]","\frac{x \sqrt[4]{\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}} \, _2F_1\left(\frac{1}{4},\frac{1}{3};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{c \sqrt[4]{a+b x^3} \sqrt[12]{c+d x^3}}","\frac{x \sqrt[4]{\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}} \, _2F_1\left(\frac{1}{4},\frac{1}{3};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{c \sqrt[4]{a+b x^3} \sqrt[12]{c+d x^3}}",1,"(x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(1/4)*Hypergeometric2F1[1/4, 1/3, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(c*(a + b*x^3)^(1/4)*(c + d*x^3)^(1/12))","A",1,1,23,0.04348,1,"{380}"
127,1,87,0,0.0173785,"\int \frac{1}{\left(a+b x^3\right)^{3/4} \left(c+d x^3\right)^{7/12}} \, dx","Int[1/((a + b*x^3)^(3/4)*(c + d*x^3)^(7/12)),x]","\frac{x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{c \left(a+b x^3\right)^{3/4}}","\frac{x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{c \left(a+b x^3\right)^{3/4}}",1,"(x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(3/4)*(c + d*x^3)^(5/12)*Hypergeometric2F1[1/3, 3/4, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(c*(a + b*x^3)^(3/4))","A",1,1,23,0.04348,1,"{380}"
128,1,87,0,0.0163963,"\int \frac{1}{\left(a+b x^3\right)^{5/4} \sqrt[12]{c+d x^3}} \, dx","Int[1/((a + b*x^3)^(5/4)*(c + d*x^3)^(1/12)),x]","\frac{x \left(c+d x^3\right)^{11/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{5/4} \, _2F_1\left(\frac{1}{3},\frac{5}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{c \left(a+b x^3\right)^{5/4}}","\frac{x \left(c+d x^3\right)^{11/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{5/4} \, _2F_1\left(\frac{1}{3},\frac{5}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{c \left(a+b x^3\right)^{5/4}}",1,"(x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(5/4)*(c + d*x^3)^(11/12)*Hypergeometric2F1[1/3, 5/4, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(c*(a + b*x^3)^(5/4))","A",1,1,23,0.04348,1,"{380}"
129,1,121,0,0.0373702,"\int \frac{\left(c+d x^3\right)^{5/12}}{\left(a+b x^3\right)^{7/4}} \, dx","Int[(c + d*x^3)^(5/12)/(a + b*x^3)^(7/4),x]","\frac{5 x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{9 a \left(a+b x^3\right)^{3/4}}+\frac{4 x \left(c+d x^3\right)^{5/12}}{9 a \left(a+b x^3\right)^{3/4}}","\frac{5 x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{9 a \left(a+b x^3\right)^{3/4}}+\frac{4 x \left(c+d x^3\right)^{5/12}}{9 a \left(a+b x^3\right)^{3/4}}",1,"(4*x*(c + d*x^3)^(5/12))/(9*a*(a + b*x^3)^(3/4)) + (5*x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(3/4)*(c + d*x^3)^(5/12)*Hypergeometric2F1[1/3, 3/4, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(9*a*(a + b*x^3)^(3/4))","A",2,2,23,0.08696,1,"{378, 380}"
130,1,121,0,0.0349659,"\int \frac{\left(c+d x^3\right)^{11/12}}{\left(a+b x^3\right)^{9/4}} \, dx","Int[(c + d*x^3)^(11/12)/(a + b*x^3)^(9/4),x]","\frac{11 x \left(c+d x^3\right)^{11/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{5/4} \, _2F_1\left(\frac{1}{3},\frac{5}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{15 a \left(a+b x^3\right)^{5/4}}+\frac{4 x \left(c+d x^3\right)^{11/12}}{15 a \left(a+b x^3\right)^{5/4}}","\frac{11 x \left(c+d x^3\right)^{11/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{5/4} \, _2F_1\left(\frac{1}{3},\frac{5}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{15 a \left(a+b x^3\right)^{5/4}}+\frac{4 x \left(c+d x^3\right)^{11/12}}{15 a \left(a+b x^3\right)^{5/4}}",1,"(4*x*(c + d*x^3)^(11/12))/(15*a*(a + b*x^3)^(5/4)) + (11*x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(5/4)*(c + d*x^3)^(11/12)*Hypergeometric2F1[1/3, 5/4, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(15*a*(a + b*x^3)^(5/4))","A",2,2,23,0.08696,1,"{378, 380}"
131,1,153,0,0.0548961,"\int \frac{\left(c+d x^3\right)^{17/12}}{\left(a+b x^3\right)^{11/4}} \, dx","Int[(c + d*x^3)^(17/12)/(a + b*x^3)^(11/4),x]","\frac{85 c x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{189 a^2 \left(a+b x^3\right)^{3/4}}+\frac{68 c x \left(c+d x^3\right)^{5/12}}{189 a^2 \left(a+b x^3\right)^{3/4}}+\frac{4 x \left(c+d x^3\right)^{17/12}}{21 a \left(a+b x^3\right)^{7/4}}","\frac{85 c x \left(c+d x^3\right)^{5/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{3/4} \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{189 a^2 \left(a+b x^3\right)^{3/4}}+\frac{68 c x \left(c+d x^3\right)^{5/12}}{189 a^2 \left(a+b x^3\right)^{3/4}}+\frac{4 x \left(c+d x^3\right)^{17/12}}{21 a \left(a+b x^3\right)^{7/4}}",1,"(68*c*x*(c + d*x^3)^(5/12))/(189*a^2*(a + b*x^3)^(3/4)) + (4*x*(c + d*x^3)^(17/12))/(21*a*(a + b*x^3)^(7/4)) + (85*c*x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(3/4)*(c + d*x^3)^(5/12)*Hypergeometric2F1[1/3, 3/4, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(189*a^2*(a + b*x^3)^(3/4))","A",3,2,23,0.08696,1,"{378, 380}"
132,1,153,0,0.0565592,"\int \frac{\left(c+d x^3\right)^{23/12}}{\left(a+b x^3\right)^{13/4}} \, dx","Int[(c + d*x^3)^(23/12)/(a + b*x^3)^(13/4),x]","\frac{253 c x \left(c+d x^3\right)^{11/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{5/4} \, _2F_1\left(\frac{1}{3},\frac{5}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{405 a^2 \left(a+b x^3\right)^{5/4}}+\frac{92 c x \left(c+d x^3\right)^{11/12}}{405 a^2 \left(a+b x^3\right)^{5/4}}+\frac{4 x \left(c+d x^3\right)^{23/12}}{27 a \left(a+b x^3\right)^{9/4}}","\frac{253 c x \left(c+d x^3\right)^{11/12} \left(\frac{c \left(a+b x^3\right)}{a \left(c+d x^3\right)}\right)^{5/4} \, _2F_1\left(\frac{1}{3},\frac{5}{4};\frac{4}{3};-\frac{(b c-a d) x^3}{a \left(d x^3+c\right)}\right)}{405 a^2 \left(a+b x^3\right)^{5/4}}+\frac{92 c x \left(c+d x^3\right)^{11/12}}{405 a^2 \left(a+b x^3\right)^{5/4}}+\frac{4 x \left(c+d x^3\right)^{23/12}}{27 a \left(a+b x^3\right)^{9/4}}",1,"(92*c*x*(c + d*x^3)^(11/12))/(405*a^2*(a + b*x^3)^(5/4)) + (4*x*(c + d*x^3)^(23/12))/(27*a*(a + b*x^3)^(9/4)) + (253*c*x*((c*(a + b*x^3))/(a*(c + d*x^3)))^(5/4)*(c + d*x^3)^(11/12)*Hypergeometric2F1[1/3, 5/4, 4/3, -(((b*c - a*d)*x^3)/(a*(c + d*x^3)))])/(405*a^2*(a + b*x^3)^(5/4))","A",3,2,23,0.08696,1,"{378, 380}"
133,1,79,0,0.0417169,"\int \left(a+b x^3\right)^m \left(c+d x^3\right)^p \, dx","Int[(a + b*x^3)^m*(c + d*x^3)^p,x]","x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \left(c+d x^3\right)^p \left(\frac{d x^3}{c}+1\right)^{-p} F_1\left(\frac{1}{3};-m,-p;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)","x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \left(c+d x^3\right)^p \left(\frac{d x^3}{c}+1\right)^{-p} F_1\left(\frac{1}{3};-m,-p;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)",1,"(x*(a + b*x^3)^m*(c + d*x^3)^p*AppellF1[1/3, -m, -p, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/((1 + (b*x^3)/a)^m*(1 + (d*x^3)/c)^p)","A",3,2,19,0.1053,1,"{430, 429}"
134,1,176,0,0.125828,"\int \left(a+b x^3\right)^2 \left(c+d x^3\right)^q \, dx","Int[(a + b*x^3)^2*(c + d*x^3)^q,x]","\frac{x \left(c+d x^3\right)^q \left(\frac{d x^3}{c}+1\right)^{-q} \left(a^2 d^2 \left(9 q^2+33 q+28\right)-2 a b c d (3 q+7)+4 b^2 c^2\right) \, _2F_1\left(\frac{1}{3},-q;\frac{4}{3};-\frac{d x^3}{c}\right)}{d^2 (3 q+4) (3 q+7)}-\frac{b x \left(c+d x^3\right)^{q+1} (4 b c-a d (3 q+10))}{d^2 (3 q+4) (3 q+7)}+\frac{b x \left(a+b x^3\right) \left(c+d x^3\right)^{q+1}}{d (3 q+7)}","\frac{x \left(c+d x^3\right)^{q+1} \left(a^2 d^2 \left(9 q^2+33 q+28\right)-2 a b c d (3 q+7)+4 b^2 c^2\right) \, _2F_1\left(1,q+\frac{4}{3};\frac{4}{3};-\frac{d x^3}{c}\right)}{c d^2 (3 q+4) (3 q+7)}-\frac{b x \left(c+d x^3\right)^{q+1} (4 b c-a d (3 q+10))}{d^2 (3 q+4) (3 q+7)}+\frac{b x \left(a+b x^3\right) \left(c+d x^3\right)^{q+1}}{d (3 q+7)}",1,"-((b*(4*b*c - a*d*(10 + 3*q))*x*(c + d*x^3)^(1 + q))/(d^2*(4 + 3*q)*(7 + 3*q))) + (b*x*(a + b*x^3)*(c + d*x^3)^(1 + q))/(d*(7 + 3*q)) + ((4*b^2*c^2 - 2*a*b*c*d*(7 + 3*q) + a^2*d^2*(28 + 33*q + 9*q^2))*x*(c + d*x^3)^q*Hypergeometric2F1[1/3, -q, 4/3, -((d*x^3)/c)])/(d^2*(4 + 3*q)*(7 + 3*q)*(1 + (d*x^3)/c)^q)","A",4,4,19,0.2105,1,"{416, 388, 246, 245}"
135,1,85,0,0.0388256,"\int \left(a+b x^3\right) \left(c+d x^3\right)^q \, dx","Int[(a + b*x^3)*(c + d*x^3)^q,x]","x \left(c+d x^3\right)^q \left(\frac{d x^3}{c}+1\right)^{-q} \left(a-\frac{b c}{3 d q+4 d}\right) \, _2F_1\left(\frac{1}{3},-q;\frac{4}{3};-\frac{d x^3}{c}\right)+\frac{b x \left(c+d x^3\right)^{q+1}}{d (3 q+4)}","\frac{b x \left(c+d x^3\right)^{q+1}}{d (3 q+4)}-\frac{x \left(c+d x^3\right)^{q+1} (b c-a d (3 q+4)) \, _2F_1\left(1,q+\frac{4}{3};\frac{4}{3};-\frac{d x^3}{c}\right)}{c d (3 q+4)}",1,"(b*x*(c + d*x^3)^(1 + q))/(d*(4 + 3*q)) + ((a - (b*c)/(4*d + 3*d*q))*x*(c + d*x^3)^q*Hypergeometric2F1[1/3, -q, 4/3, -((d*x^3)/c)])/(1 + (d*x^3)/c)^q","A",3,3,17,0.1765,1,"{388, 246, 245}"
136,1,57,0,0.0271866,"\int \frac{\left(c+d x^3\right)^q}{a+b x^3} \, dx","Int[(c + d*x^3)^q/(a + b*x^3),x]","\frac{x \left(c+d x^3\right)^q \left(\frac{d x^3}{c}+1\right)^{-q} F_1\left(\frac{1}{3};1,-q;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a}","\frac{x \left(c+d x^3\right)^q \left(\frac{d x^3}{c}+1\right)^{-q} F_1\left(\frac{1}{3};1,-q;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a}",1,"(x*(c + d*x^3)^q*AppellF1[1/3, 1, -q, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*(1 + (d*x^3)/c)^q)","A",2,2,19,0.1053,1,"{430, 429}"
137,1,57,0,0.0273022,"\int \frac{\left(c+d x^3\right)^q}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^q/(a + b*x^3)^2,x]","\frac{x \left(c+d x^3\right)^q \left(\frac{d x^3}{c}+1\right)^{-q} F_1\left(\frac{1}{3};2,-q;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2}","\frac{x \left(c+d x^3\right)^q \left(\frac{d x^3}{c}+1\right)^{-q} F_1\left(\frac{1}{3};2,-q;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2}",1,"(x*(c + d*x^3)^q*AppellF1[1/3, 2, -q, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*(1 + (d*x^3)/c)^q)","A",2,2,19,0.1053,1,"{430, 429}"
138,1,298,0,0.3038789,"\int \left(a+b x^3\right)^m \left(c+d x^3\right)^3 \, dx","Int[(a + b*x^3)^m*(c + d*x^3)^3,x]","-\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \left(-12 a^2 b c d^2 (3 m+10)+28 a^3 d^3+3 a b^2 c^2 d \left(9 m^2+51 m+70\right)-b^3 c^3 \left(27 m^3+189 m^2+414 m+280\right)\right) \, _2F_1\left(\frac{1}{3},-m;\frac{4}{3};-\frac{b x^3}{a}\right)}{b^3 (3 m+4) (3 m+7) (3 m+10)}+\frac{d x \left(a+b x^3\right)^{m+1} \left(28 a^2 d^2-a b c d (15 m+92)+b^2 c^2 \left(9 m^2+60 m+118\right)\right)}{b^3 (3 m+4) (3 m+7) (3 m+10)}-\frac{d x \left(c+d x^3\right) \left(a+b x^3\right)^{m+1} (7 a d-b c (3 m+16))}{b^2 (3 m+7) (3 m+10)}+\frac{d x \left(c+d x^3\right)^2 \left(a+b x^3\right)^{m+1}}{b (3 m+10)}","-\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \left(-12 a^2 b c d^2 (3 m+10)+28 a^3 d^3+3 a b^2 c^2 d \left(9 m^2+51 m+70\right)-b^3 c^3 \left(27 m^3+189 m^2+414 m+280\right)\right) \, _2F_1\left(\frac{1}{3},-m;\frac{4}{3};-\frac{b x^3}{a}\right)}{b^3 (3 m+4) (3 m+7) (3 m+10)}+\frac{d x \left(a+b x^3\right)^{m+1} \left(28 a^2 d^2-a b c d (15 m+92)+b^2 c^2 \left(9 m^2+60 m+118\right)\right)}{b^3 (3 m+4) (3 m+7) (3 m+10)}-\frac{d x \left(c+d x^3\right) \left(a+b x^3\right)^{m+1} (7 a d-b c (3 m+16))}{b^2 (3 m+7) (3 m+10)}+\frac{d x \left(c+d x^3\right)^2 \left(a+b x^3\right)^{m+1}}{b (3 m+10)}",1,"(d*(28*a^2*d^2 - a*b*c*d*(92 + 15*m) + b^2*c^2*(118 + 60*m + 9*m^2))*x*(a + b*x^3)^(1 + m))/(b^3*(4 + 3*m)*(7 + 3*m)*(10 + 3*m)) - (d*(7*a*d - b*c*(16 + 3*m))*x*(a + b*x^3)^(1 + m)*(c + d*x^3))/(b^2*(7 + 3*m)*(10 + 3*m)) + (d*x*(a + b*x^3)^(1 + m)*(c + d*x^3)^2)/(b*(10 + 3*m)) - ((28*a^3*d^3 - 12*a^2*b*c*d^2*(10 + 3*m) + 3*a*b^2*c^2*d*(70 + 51*m + 9*m^2) - b^3*c^3*(280 + 414*m + 189*m^2 + 27*m^3))*x*(a + b*x^3)^m*Hypergeometric2F1[1/3, -m, 4/3, -((b*x^3)/a)])/(b^3*(4 + 3*m)*(7 + 3*m)*(10 + 3*m)*(1 + (b*x^3)/a)^m)","A",5,5,19,0.2632,1,"{416, 528, 388, 246, 245}"
139,1,176,0,0.1257313,"\int \left(a+b x^3\right)^m \left(c+d x^3\right)^2 \, dx","Int[(a + b*x^3)^m*(c + d*x^3)^2,x]","\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \left(4 a^2 d^2-2 a b c d (3 m+7)+b^2 c^2 \left(9 m^2+33 m+28\right)\right) \, _2F_1\left(\frac{1}{3},-m;\frac{4}{3};-\frac{b x^3}{a}\right)}{b^2 (3 m+4) (3 m+7)}-\frac{d x \left(a+b x^3\right)^{m+1} (4 a d-b c (3 m+10))}{b^2 (3 m+4) (3 m+7)}+\frac{d x \left(c+d x^3\right) \left(a+b x^3\right)^{m+1}}{b (3 m+7)}","\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \left(4 a^2 d^2-2 a b c d (3 m+7)+b^2 c^2 \left(9 m^2+33 m+28\right)\right) \, _2F_1\left(\frac{1}{3},-m;\frac{4}{3};-\frac{b x^3}{a}\right)}{b^2 (3 m+4) (3 m+7)}-\frac{d x \left(a+b x^3\right)^{m+1} (4 a d-b c (3 m+10))}{b^2 (3 m+4) (3 m+7)}+\frac{d x \left(c+d x^3\right) \left(a+b x^3\right)^{m+1}}{b (3 m+7)}",1,"-((d*(4*a*d - b*c*(10 + 3*m))*x*(a + b*x^3)^(1 + m))/(b^2*(4 + 3*m)*(7 + 3*m))) + (d*x*(a + b*x^3)^(1 + m)*(c + d*x^3))/(b*(7 + 3*m)) + ((4*a^2*d^2 - 2*a*b*c*d*(7 + 3*m) + b^2*c^2*(28 + 33*m + 9*m^2))*x*(a + b*x^3)^m*Hypergeometric2F1[1/3, -m, 4/3, -((b*x^3)/a)])/(b^2*(4 + 3*m)*(7 + 3*m)*(1 + (b*x^3)/a)^m)","A",4,4,19,0.2105,1,"{416, 388, 246, 245}"
140,1,85,0,0.0424879,"\int \left(a+b x^3\right)^m \left(c+d x^3\right) \, dx","Int[(a + b*x^3)^m*(c + d*x^3),x]","x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \left(c-\frac{a d}{3 b m+4 b}\right) \, _2F_1\left(\frac{1}{3},-m;\frac{4}{3};-\frac{b x^3}{a}\right)+\frac{d x \left(a+b x^3\right)^{m+1}}{b (3 m+4)}","\frac{d x \left(a+b x^3\right)^{m+1}}{b (3 m+4)}-\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} (a d-b c (3 m+4)) \, _2F_1\left(\frac{1}{3},-m;\frac{4}{3};-\frac{b x^3}{a}\right)}{b (3 m+4)}",1,"(d*x*(a + b*x^3)^(1 + m))/(b*(4 + 3*m)) + ((c - (a*d)/(4*b + 3*b*m))*x*(a + b*x^3)^m*Hypergeometric2F1[1/3, -m, 4/3, -((b*x^3)/a)])/(1 + (b*x^3)/a)^m","A",3,3,17,0.1765,1,"{388, 246, 245}"
141,1,44,0,0.0101219,"\int \left(a+b x^3\right)^m \, dx","Int[(a + b*x^3)^m,x]","x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \, _2F_1\left(\frac{1}{3},-m;\frac{4}{3};-\frac{b x^3}{a}\right)","x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} \, _2F_1\left(\frac{1}{3},-m;\frac{4}{3};-\frac{b x^3}{a}\right)",1,"(x*(a + b*x^3)^m*Hypergeometric2F1[1/3, -m, 4/3, -((b*x^3)/a)])/(1 + (b*x^3)/a)^m","A",2,2,9,0.2222,1,"{246, 245}"
142,1,57,0,0.0251674,"\int \frac{\left(a+b x^3\right)^m}{c+d x^3} \, dx","Int[(a + b*x^3)^m/(c + d*x^3),x]","\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} F_1\left(\frac{1}{3};-m,1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c}","\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} F_1\left(\frac{1}{3};-m,1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c}",1,"(x*(a + b*x^3)^m*AppellF1[1/3, -m, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^m)","A",2,2,19,0.1053,1,"{430, 429}"
143,1,57,0,0.0249284,"\int \frac{\left(a+b x^3\right)^m}{\left(c+d x^3\right)^2} \, dx","Int[(a + b*x^3)^m/(c + d*x^3)^2,x]","\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} F_1\left(\frac{1}{3};-m,2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2}","\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} F_1\left(\frac{1}{3};-m,2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^2}",1,"(x*(a + b*x^3)^m*AppellF1[1/3, -m, 2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^2*(1 + (b*x^3)/a)^m)","A",2,2,19,0.1053,1,"{430, 429}"
144,1,57,0,0.0270919,"\int \frac{\left(a+b x^3\right)^m}{\left(c+d x^3\right)^3} \, dx","Int[(a + b*x^3)^m/(c + d*x^3)^3,x]","\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} F_1\left(\frac{1}{3};-m,3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3}","\frac{x \left(a+b x^3\right)^m \left(\frac{b x^3}{a}+1\right)^{-m} F_1\left(\frac{1}{3};-m,3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c^3}",1,"(x*(a + b*x^3)^m*AppellF1[1/3, -m, 3, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c^3*(1 + (b*x^3)/a)^m)","A",2,2,19,0.1053,1,"{430, 429}"
145,1,53,0,0.019047,"\int \left(a+b x^3\right)^{-1-\frac{b c}{3 b c-3 a d}} \left(c+d x^3\right)^{-1+\frac{a d}{3 b c-3 a d}} \, dx","Int[(a + b*x^3)^(-1 - (b*c)/(3*b*c - 3*a*d))*(c + d*x^3)^(-1 + (a*d)/(3*b*c - 3*a*d)),x]","\frac{x \left(a+b x^3\right)^{-\frac{b c}{3 b c-3 a d}} \left(c+d x^3\right)^{\frac{a d}{3 b c-3 a d}}}{a c}","\frac{x \left(a+b x^3\right)^{-\frac{b c}{3 b c-3 a d}} \left(c+d x^3\right)^{\frac{a d}{3 b c-3 a d}}}{a c}",1,"(x*(c + d*x^3)^((a*d)/(3*b*c - 3*a*d)))/(a*c*(a + b*x^3)^((b*c)/(3*b*c - 3*a*d)))","A",1,1,50,0.02000,1,"{381}"
146,1,94,0,0.0676504,"\int \left(a+b x^4\right) \left(c+d x^4\right)^4 \, dx","Int[(a + b*x^4)*(c + d*x^4)^4,x]","\frac{2}{9} c^2 d x^9 (3 a d+2 b c)+\frac{1}{5} c^3 x^5 (4 a d+b c)+\frac{1}{17} d^3 x^{17} (a d+4 b c)+\frac{2}{13} c d^2 x^{13} (2 a d+3 b c)+a c^4 x+\frac{1}{21} b d^4 x^{21}","\frac{2}{9} c^2 d x^9 (3 a d+2 b c)+\frac{1}{5} c^3 x^5 (4 a d+b c)+\frac{1}{17} d^3 x^{17} (a d+4 b c)+\frac{2}{13} c d^2 x^{13} (2 a d+3 b c)+a c^4 x+\frac{1}{21} b d^4 x^{21}",1,"a*c^4*x + (c^3*(b*c + 4*a*d)*x^5)/5 + (2*c^2*d*(2*b*c + 3*a*d)*x^9)/9 + (2*c*d^2*(3*b*c + 2*a*d)*x^13)/13 + (d^3*(4*b*c + a*d)*x^17)/17 + (b*d^4*x^21)/21","A",2,1,17,0.05882,1,"{373}"
147,1,70,0,0.0487288,"\int \left(a+b x^4\right) \left(c+d x^4\right)^3 \, dx","Int[(a + b*x^4)*(c + d*x^4)^3,x]","\frac{1}{5} c^2 x^5 (3 a d+b c)+\frac{1}{13} d^2 x^{13} (a d+3 b c)+\frac{1}{3} c d x^9 (a d+b c)+a c^3 x+\frac{1}{17} b d^3 x^{17}","\frac{1}{5} c^2 x^5 (3 a d+b c)+\frac{1}{13} d^2 x^{13} (a d+3 b c)+\frac{1}{3} c d x^9 (a d+b c)+a c^3 x+\frac{1}{17} b d^3 x^{17}",1,"a*c^3*x + (c^2*(b*c + 3*a*d)*x^5)/5 + (c*d*(b*c + a*d)*x^9)/3 + (d^2*(3*b*c + a*d)*x^13)/13 + (b*d^3*x^17)/17","A",2,1,17,0.05882,1,"{373}"
148,1,50,0,0.029443,"\int \left(a+b x^4\right) \left(c+d x^4\right)^2 \, dx","Int[(a + b*x^4)*(c + d*x^4)^2,x]","\frac{1}{9} d x^9 (a d+2 b c)+\frac{1}{5} c x^5 (2 a d+b c)+a c^2 x+\frac{1}{13} b d^2 x^{13}","\frac{1}{9} d x^9 (a d+2 b c)+\frac{1}{5} c x^5 (2 a d+b c)+a c^2 x+\frac{1}{13} b d^2 x^{13}",1,"a*c^2*x + (c*(b*c + 2*a*d)*x^5)/5 + (d*(2*b*c + a*d)*x^9)/9 + (b*d^2*x^13)/13","A",2,1,17,0.05882,1,"{373}"
149,1,28,0,0.0144161,"\int \left(a+b x^4\right) \left(c+d x^4\right) \, dx","Int[(a + b*x^4)*(c + d*x^4),x]","\frac{1}{5} x^5 (a d+b c)+a c x+\frac{1}{9} b d x^9","\frac{1}{5} x^5 (a d+b c)+a c x+\frac{1}{9} b d x^9",1,"a*c*x + ((b*c + a*d)*x^5)/5 + (b*d*x^9)/9","A",2,1,15,0.06667,1,"{373}"
150,1,223,0,0.1513683,"\int \frac{a+b x^4}{c+d x^4} \, dx","Int[(a + b*x^4)/(c + d*x^4),x]","\frac{(b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} d^{5/4}}-\frac{(b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} d^{5/4}}+\frac{(b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} d^{5/4}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} d^{5/4}}+\frac{b x}{d}","\frac{(b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} d^{5/4}}-\frac{(b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} d^{5/4}}+\frac{(b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} d^{5/4}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} d^{5/4}}+\frac{b x}{d}",1,"(b*x)/d + ((b*c - a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*d^(5/4)) - ((b*c - a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*d^(5/4)) + ((b*c - a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*d^(5/4)) - ((b*c - a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*d^(5/4))","A",10,7,17,0.4118,1,"{388, 211, 1165, 628, 1162, 617, 204}"
151,1,245,0,0.1465783,"\int \frac{a+b x^4}{\left(c+d x^4\right)^2} \, dx","Int[(a + b*x^4)/(c + d*x^4)^2,x]","-\frac{(3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} d^{5/4}}+\frac{(3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} d^{5/4}}-\frac{(3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{8 \sqrt{2} c^{7/4} d^{5/4}}+\frac{(3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{8 \sqrt{2} c^{7/4} d^{5/4}}-\frac{x (b c-a d)}{4 c d \left(c+d x^4\right)}","-\frac{(3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} d^{5/4}}+\frac{(3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} d^{5/4}}-\frac{(3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{8 \sqrt{2} c^{7/4} d^{5/4}}+\frac{(3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{8 \sqrt{2} c^{7/4} d^{5/4}}-\frac{x (b c-a d)}{4 c d \left(c+d x^4\right)}",1,"-((b*c - a*d)*x)/(4*c*d*(c + d*x^4)) - ((b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(8*Sqrt[2]*c^(7/4)*d^(5/4)) + ((b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(8*Sqrt[2]*c^(7/4)*d^(5/4)) - ((b*c + 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(16*Sqrt[2]*c^(7/4)*d^(5/4)) + ((b*c + 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(16*Sqrt[2]*c^(7/4)*d^(5/4))","A",10,7,17,0.4118,1,"{385, 211, 1165, 628, 1162, 617, 204}"
152,1,273,0,0.1742767,"\int \frac{a+b x^4}{\left(c+d x^4\right)^3} \, dx","Int[(a + b*x^4)/(c + d*x^4)^3,x]","-\frac{3 (7 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{128 \sqrt{2} c^{11/4} d^{5/4}}+\frac{3 (7 a d+b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{128 \sqrt{2} c^{11/4} d^{5/4}}-\frac{3 (7 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{64 \sqrt{2} c^{11/4} d^{5/4}}+\frac{3 (7 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{64 \sqrt{2} c^{11/4} d^{5/4}}+\frac{x (7 a d+b c)}{32 c^2 d \left(c+d x^4\right)}-\frac{x (b c-a d)}{8 c d \left(c+d x^4\right)^2}","-\frac{3 (7 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{128 \sqrt{2} c^{11/4} d^{5/4}}+\frac{3 (7 a d+b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{128 \sqrt{2} c^{11/4} d^{5/4}}-\frac{3 (7 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{64 \sqrt{2} c^{11/4} d^{5/4}}+\frac{3 (7 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{64 \sqrt{2} c^{11/4} d^{5/4}}+\frac{x (7 a d+b c)}{32 c^2 d \left(c+d x^4\right)}-\frac{x (b c-a d)}{8 c d \left(c+d x^4\right)^2}",1,"-((b*c - a*d)*x)/(8*c*d*(c + d*x^4)^2) + ((b*c + 7*a*d)*x)/(32*c^2*d*(c + d*x^4)) - (3*(b*c + 7*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(64*Sqrt[2]*c^(11/4)*d^(5/4)) + (3*(b*c + 7*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(64*Sqrt[2]*c^(11/4)*d^(5/4)) - (3*(b*c + 7*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(128*Sqrt[2]*c^(11/4)*d^(5/4)) + (3*(b*c + 7*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(128*Sqrt[2]*c^(11/4)*d^(5/4))","A",11,8,17,0.4706,1,"{385, 199, 211, 1165, 628, 1162, 617, 204}"
153,1,154,0,0.1139425,"\int \left(a+b x^4\right)^2 \left(c+d x^4\right)^4 \, dx","Int[(a + b*x^4)^2*(c + d*x^4)^4,x]","\frac{1}{17} d^2 x^{17} \left(a^2 d^2+8 a b c d+6 b^2 c^2\right)+\frac{4}{13} c d x^{13} \left(a^2 d^2+3 a b c d+b^2 c^2\right)+\frac{1}{9} c^2 x^9 \left(6 a^2 d^2+8 a b c d+b^2 c^2\right)+a^2 c^4 x+\frac{2}{5} a c^3 x^5 (2 a d+b c)+\frac{2}{21} b d^3 x^{21} (a d+2 b c)+\frac{1}{25} b^2 d^4 x^{25}","\frac{1}{17} d^2 x^{17} \left(a^2 d^2+8 a b c d+6 b^2 c^2\right)+\frac{4}{13} c d x^{13} \left(a^2 d^2+3 a b c d+b^2 c^2\right)+\frac{1}{9} c^2 x^9 \left(6 a^2 d^2+8 a b c d+b^2 c^2\right)+a^2 c^4 x+\frac{2}{5} a c^3 x^5 (2 a d+b c)+\frac{2}{21} b d^3 x^{21} (a d+2 b c)+\frac{1}{25} b^2 d^4 x^{25}",1,"a^2*c^4*x + (2*a*c^3*(b*c + 2*a*d)*x^5)/5 + (c^2*(b^2*c^2 + 8*a*b*c*d + 6*a^2*d^2)*x^9)/9 + (4*c*d*(b^2*c^2 + 3*a*b*c*d + a^2*d^2)*x^13)/13 + (d^2*(6*b^2*c^2 + 8*a*b*c*d + a^2*d^2)*x^17)/17 + (2*b*d^3*(2*b*c + a*d)*x^21)/21 + (b^2*d^4*x^25)/25","A",2,1,19,0.05263,1,"{373}"
154,1,122,0,0.0766227,"\int \left(a+b x^4\right)^2 \left(c+d x^4\right)^3 \, dx","Int[(a + b*x^4)^2*(c + d*x^4)^3,x]","\frac{1}{13} d x^{13} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{9} c x^9 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 x+\frac{1}{5} a c^2 x^5 (3 a d+2 b c)+\frac{1}{17} b d^2 x^{17} (2 a d+3 b c)+\frac{1}{21} b^2 d^3 x^{21}","\frac{1}{13} d x^{13} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{9} c x^9 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 x+\frac{1}{5} a c^2 x^5 (3 a d+2 b c)+\frac{1}{17} b d^2 x^{17} (2 a d+3 b c)+\frac{1}{21} b^2 d^3 x^{21}",1,"a^2*c^3*x + (a*c^2*(2*b*c + 3*a*d)*x^5)/5 + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^9)/9 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^13)/13 + (b*d^2*(3*b*c + 2*a*d)*x^17)/17 + (b^2*d^3*x^21)/21","A",2,1,19,0.05263,1,"{373}"
155,1,82,0,0.0491069,"\int \left(a+b x^4\right)^2 \left(c+d x^4\right)^2 \, dx","Int[(a + b*x^4)^2*(c + d*x^4)^2,x]","\frac{1}{9} x^9 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 x+\frac{2}{13} b d x^{13} (a d+b c)+\frac{2}{5} a c x^5 (a d+b c)+\frac{1}{17} b^2 d^2 x^{17}","\frac{1}{9} x^9 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 x+\frac{2}{13} b d x^{13} (a d+b c)+\frac{2}{5} a c x^5 (a d+b c)+\frac{1}{17} b^2 d^2 x^{17}",1,"a^2*c^2*x + (2*a*c*(b*c + a*d)*x^5)/5 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^9)/9 + (2*b*d*(b*c + a*d)*x^13)/13 + (b^2*d^2*x^17)/17","A",2,1,19,0.05263,1,"{373}"
156,1,50,0,0.0302635,"\int \left(a+b x^4\right)^2 \left(c+d x^4\right) \, dx","Int[(a + b*x^4)^2*(c + d*x^4),x]","a^2 c x+\frac{1}{9} b x^9 (2 a d+b c)+\frac{1}{5} a x^5 (a d+2 b c)+\frac{1}{13} b^2 d x^{13}","a^2 c x+\frac{1}{9} b x^9 (2 a d+b c)+\frac{1}{5} a x^5 (a d+2 b c)+\frac{1}{13} b^2 d x^{13}",1,"a^2*c*x + (a*(2*b*c + a*d)*x^5)/5 + (b*(b*c + 2*a*d)*x^9)/9 + (b^2*d*x^13)/13","A",2,1,17,0.05882,1,"{373}"
157,1,253,0,0.1936565,"\int \frac{\left(a+b x^4\right)^2}{c+d x^4} \, dx","Int[(a + b*x^4)^2/(c + d*x^4),x]","-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} d^{9/4}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} d^{9/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} d^{9/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} d^{9/4}}-\frac{b x (b c-2 a d)}{d^2}+\frac{b^2 x^5}{5 d}","-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} d^{9/4}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} d^{9/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} d^{9/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} d^{9/4}}-\frac{b x (b c-2 a d)}{d^2}+\frac{b^2 x^5}{5 d}",1,"-((b*(b*c - 2*a*d)*x)/d^2) + (b^2*x^5)/(5*d) - ((b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*d^(9/4)) + ((b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*d^(9/4)) - ((b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*d^(9/4)) + ((b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*d^(9/4))","A",11,7,19,0.3684,1,"{390, 211, 1165, 628, 1162, 617, 204}"
158,1,291,0,0.3657653,"\int \frac{\left(a+b x^4\right)^2}{\left(c+d x^4\right)^2} \, dx","Int[(a + b*x^4)^2/(c + d*x^4)^2,x]","\frac{(b c-a d) (3 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} d^{9/4}}-\frac{(b c-a d) (3 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} d^{9/4}}+\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{8 \sqrt{2} c^{7/4} d^{9/4}}-\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{8 \sqrt{2} c^{7/4} d^{9/4}}+\frac{x (b c-a d)^2}{4 c d^2 \left(c+d x^4\right)}+\frac{b^2 x}{d^2}","\frac{(b c-a d) (3 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} d^{9/4}}-\frac{(b c-a d) (3 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} d^{9/4}}+\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{8 \sqrt{2} c^{7/4} d^{9/4}}-\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{8 \sqrt{2} c^{7/4} d^{9/4}}+\frac{x (b c-a d)^2}{4 c d^2 \left(c+d x^4\right)}+\frac{b^2 x}{d^2}",1,"(b^2*x)/d^2 + ((b*c - a*d)^2*x)/(4*c*d^2*(c + d*x^4)) + ((b*c - a*d)*(5*b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(8*Sqrt[2]*c^(7/4)*d^(9/4)) - ((b*c - a*d)*(5*b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(8*Sqrt[2]*c^(7/4)*d^(9/4)) + ((b*c - a*d)*(5*b*c + 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(16*Sqrt[2]*c^(7/4)*d^(9/4)) - ((b*c - a*d)*(5*b*c + 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(16*Sqrt[2]*c^(7/4)*d^(9/4))","A",12,8,19,0.4211,1,"{390, 385, 211, 1165, 628, 1162, 617, 204}"
159,1,349,0,0.2656174,"\int \frac{\left(a+b x^4\right)^2}{\left(c+d x^4\right)^3} \, dx","Int[(a + b*x^4)^2/(c + d*x^4)^3,x]","-\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{128 \sqrt{2} c^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{128 \sqrt{2} c^{11/4} d^{9/4}}-\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{64 \sqrt{2} c^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{64 \sqrt{2} c^{11/4} d^{9/4}}-\frac{x (b c-a d) (7 a d+5 b c)}{32 c^2 d^2 \left(c+d x^4\right)}-\frac{x \left(a+b x^4\right) (b c-a d)}{8 c d \left(c+d x^4\right)^2}","-\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{128 \sqrt{2} c^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{128 \sqrt{2} c^{11/4} d^{9/4}}-\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{64 \sqrt{2} c^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{64 \sqrt{2} c^{11/4} d^{9/4}}-\frac{x (b c-a d) (7 a d+5 b c)}{32 c^2 d^2 \left(c+d x^4\right)}-\frac{x \left(a+b x^4\right) (b c-a d)}{8 c d \left(c+d x^4\right)^2}",1,"-((b*c - a*d)*x*(a + b*x^4))/(8*c*d*(c + d*x^4)^2) - ((b*c - a*d)*(5*b*c + 7*a*d)*x)/(32*c^2*d^2*(c + d*x^4)) - ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(64*Sqrt[2]*c^(11/4)*d^(9/4)) + ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(64*Sqrt[2]*c^(11/4)*d^(9/4)) - ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(128*Sqrt[2]*c^(11/4)*d^(9/4)) + ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(128*Sqrt[2]*c^(11/4)*d^(9/4))","A",11,8,19,0.4211,1,"{413, 385, 211, 1165, 628, 1162, 617, 204}"
160,1,332,0,0.2666369,"\int \frac{\left(c+d x^4\right)^4}{a+b x^4} \, dx","Int[(c + d*x^4)^4/(a + b*x^4),x]","\frac{d^2 x^5 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right)}{5 b^3}+\frac{d x (2 b c-a d) \left(a^2 d^2-2 a b c d+2 b^2 c^2\right)}{b^4}-\frac{(b c-a d)^4 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{17/4}}+\frac{(b c-a d)^4 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{17/4}}-\frac{(b c-a d)^4 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{17/4}}+\frac{(b c-a d)^4 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{17/4}}+\frac{d^3 x^9 (4 b c-a d)}{9 b^2}+\frac{d^4 x^{13}}{13 b}","\frac{d^2 x^5 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right)}{5 b^3}+\frac{d x (2 b c-a d) \left(a^2 d^2-2 a b c d+2 b^2 c^2\right)}{b^4}-\frac{(b c-a d)^4 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{17/4}}+\frac{(b c-a d)^4 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{17/4}}-\frac{(b c-a d)^4 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{17/4}}+\frac{(b c-a d)^4 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{17/4}}+\frac{d^3 x^9 (4 b c-a d)}{9 b^2}+\frac{d^4 x^{13}}{13 b}",1,"(d*(2*b*c - a*d)*(2*b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/b^4 + (d^2*(6*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*x^5)/(5*b^3) + (d^3*(4*b*c - a*d)*x^9)/(9*b^2) + (d^4*x^13)/(13*b) - ((b*c - a*d)^4*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(17/4)) + ((b*c - a*d)^4*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(17/4)) - ((b*c - a*d)^4*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(17/4)) + ((b*c - a*d)^4*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(17/4))","A",11,7,19,0.3684,1,"{390, 211, 1165, 628, 1162, 617, 204}"
161,1,288,0,0.2234679,"\int \frac{\left(c+d x^4\right)^3}{a+b x^4} \, dx","Int[(c + d*x^4)^3/(a + b*x^4),x]","\frac{d x \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3}-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{13/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{13/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{13/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{13/4}}+\frac{d^2 x^5 (3 b c-a d)}{5 b^2}+\frac{d^3 x^9}{9 b}","\frac{d x \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3}-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{13/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{13/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{13/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{13/4}}+\frac{d^2 x^5 (3 b c-a d)}{5 b^2}+\frac{d^3 x^9}{9 b}",1,"(d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x)/b^3 + (d^2*(3*b*c - a*d)*x^5)/(5*b^2) + (d^3*x^9)/(9*b) - ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(13/4)) + ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(13/4)) - ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(13/4)) + ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(13/4))","A",11,7,19,0.3684,1,"{390, 211, 1165, 628, 1162, 617, 204}"
162,1,253,0,0.1901984,"\int \frac{\left(c+d x^4\right)^2}{a+b x^4} \, dx","Int[(c + d*x^4)^2/(a + b*x^4),x]","-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{9/4}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{9/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{9/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{9/4}}+\frac{d x (2 b c-a d)}{b^2}+\frac{d^2 x^5}{5 b}","-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{9/4}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{9/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{9/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{9/4}}+\frac{d x (2 b c-a d)}{b^2}+\frac{d^2 x^5}{5 b}",1,"(d*(2*b*c - a*d)*x)/b^2 + (d^2*x^5)/(5*b) - ((b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(9/4)) + ((b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(9/4)) - ((b*c - a*d)^2*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(9/4)) + ((b*c - a*d)^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(9/4))","A",11,7,19,0.3684,1,"{390, 211, 1165, 628, 1162, 617, 204}"
163,1,223,0,0.1382618,"\int \frac{c+d x^4}{a+b x^4} \, dx","Int[(c + d*x^4)/(a + b*x^4),x]","-\frac{(b c-a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{(b c-a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{(b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{d x}{b}","-\frac{(b c-a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{(b c-a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{(b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{d x}{b}",1,"(d*x)/b - ((b*c - a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(5/4)) + ((b*c - a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(5/4)) - ((b*c - a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(5/4)) + ((b*c - a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(5/4))","A",10,7,17,0.4118,1,"{388, 211, 1165, 628, 1162, 617, 204}"
164,1,449,0,0.2675215,"\int \frac{1}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)*(c + d*x^4)),x]","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)}-\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{d^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)}+\frac{d^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)}-\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{d^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)}+\frac{d^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}",1,"-(b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (d^(3/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*(b*c - a*d)) - (d^(3/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*(b*c - a*d)) - (b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (d^(3/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*(b*c - a*d)) - (d^(3/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*(b*c - a*d))","A",19,7,19,0.3684,1,"{391, 211, 1165, 628, 1162, 617, 204}"
165,1,513,0,0.4196931,"\int \frac{1}{\left(a+b x^4\right) \left(c+d x^4\right)^2} \, dx","Int[1/((a + b*x^4)*(c + d*x^4)^2),x]","-\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^2}+\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^2}-\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^2}+\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^2}+\frac{d^{3/4} (7 b c-3 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d^{3/4} (7 b c-3 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} (b c-a d)^2}+\frac{d^{3/4} (7 b c-3 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d^{3/4} (7 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d x}{4 c \left(c+d x^4\right) (b c-a d)}","-\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^2}+\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^2}-\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^2}+\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^2}+\frac{d^{3/4} (7 b c-3 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d^{3/4} (7 b c-3 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} (b c-a d)^2}+\frac{d^{3/4} (7 b c-3 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d^{3/4} (7 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d x}{4 c \left(c+d x^4\right) (b c-a d)}",1,"-(d*x)/(4*c*(b*c - a*d)*(c + d*x^4)) - (b^(7/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)^2) + (b^(7/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)^2) + (d^(3/4)*(7*b*c - 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(8*Sqrt[2]*c^(7/4)*(b*c - a*d)^2) - (d^(3/4)*(7*b*c - 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(8*Sqrt[2]*c^(7/4)*(b*c - a*d)^2) - (b^(7/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)^2) + (b^(7/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)^2) + (d^(3/4)*(7*b*c - 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(16*Sqrt[2]*c^(7/4)*(b*c - a*d)^2) - (d^(3/4)*(7*b*c - 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(16*Sqrt[2]*c^(7/4)*(b*c - a*d)^2)","A",20,8,19,0.4211,1,"{414, 522, 211, 1165, 628, 1162, 617, 204}"
166,1,407,0,0.3955487,"\int \frac{\left(c+d x^4\right)^5}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x^4)^5/(a + b*x^4)^2,x]","\frac{d^3 x^5 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right)}{5 b^4}+\frac{d^2 x \left(15 a^2 b c d^2-4 a^3 d^3-20 a b^2 c^2 d+10 b^3 c^3\right)}{b^5}-\frac{(b c-a d)^4 (17 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{21/4}}+\frac{(b c-a d)^4 (17 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{21/4}}-\frac{(b c-a d)^4 (17 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{21/4}}+\frac{(b c-a d)^4 (17 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{21/4}}+\frac{d^4 x^9 (5 b c-2 a d)}{9 b^3}+\frac{x (b c-a d)^5}{4 a b^5 \left(a+b x^4\right)}+\frac{d^5 x^{13}}{13 b^2}","\frac{d^3 x^5 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right)}{5 b^4}+\frac{d^2 x \left(15 a^2 b c d^2-4 a^3 d^3-20 a b^2 c^2 d+10 b^3 c^3\right)}{b^5}-\frac{(b c-a d)^4 (17 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{21/4}}+\frac{(b c-a d)^4 (17 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{21/4}}-\frac{(b c-a d)^4 (17 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{21/4}}+\frac{(b c-a d)^4 (17 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{21/4}}+\frac{d^4 x^9 (5 b c-2 a d)}{9 b^3}+\frac{x (b c-a d)^5}{4 a b^5 \left(a+b x^4\right)}+\frac{d^5 x^{13}}{13 b^2}",1,"(d^2*(10*b^3*c^3 - 20*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3)*x)/b^5 + (d^3*(10*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^5)/(5*b^4) + (d^4*(5*b*c - 2*a*d)*x^9)/(9*b^3) + (d^5*x^13)/(13*b^2) + ((b*c - a*d)^5*x)/(4*a*b^5*(a + b*x^4)) - ((b*c - a*d)^4*(3*b*c + 17*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(21/4)) + ((b*c - a*d)^4*(3*b*c + 17*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(21/4)) - ((b*c - a*d)^4*(3*b*c + 17*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(21/4)) + ((b*c - a*d)^4*(3*b*c + 17*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(21/4))","A",12,8,19,0.4211,1,"{390, 385, 211, 1165, 628, 1162, 617, 204}"
167,1,357,0,0.3665598,"\int \frac{\left(c+d x^4\right)^4}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x^4)^4/(a + b*x^4)^2,x]","\frac{d^2 x \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right)}{b^4}-\frac{(b c-a d)^3 (13 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{17/4}}+\frac{(b c-a d)^3 (13 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{17/4}}-\frac{(b c-a d)^3 (13 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{17/4}}+\frac{(b c-a d)^3 (13 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{17/4}}+\frac{2 d^3 x^5 (2 b c-a d)}{5 b^3}+\frac{x (b c-a d)^4}{4 a b^4 \left(a+b x^4\right)}+\frac{d^4 x^9}{9 b^2}","\frac{d^2 x \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right)}{b^4}-\frac{(b c-a d)^3 (13 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{17/4}}+\frac{(b c-a d)^3 (13 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{17/4}}-\frac{(b c-a d)^3 (13 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{17/4}}+\frac{(b c-a d)^3 (13 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{17/4}}+\frac{2 d^3 x^5 (2 b c-a d)}{5 b^3}+\frac{x (b c-a d)^4}{4 a b^4 \left(a+b x^4\right)}+\frac{d^4 x^9}{9 b^2}",1,"(d^2*(6*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*x)/b^4 + (2*d^3*(2*b*c - a*d)*x^5)/(5*b^3) + (d^4*x^9)/(9*b^2) + ((b*c - a*d)^4*x)/(4*a*b^4*(a + b*x^4)) - ((b*c - a*d)^3*(3*b*c + 13*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(17/4)) + ((b*c - a*d)^3*(3*b*c + 13*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(17/4)) - ((b*c - a*d)^3*(3*b*c + 13*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(17/4)) + ((b*c - a*d)^3*(3*b*c + 13*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(17/4))","A",12,8,19,0.4211,1,"{390, 385, 211, 1165, 628, 1162, 617, 204}"
168,1,317,0,0.3171775,"\int \frac{\left(c+d x^4\right)^3}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x^4)^3/(a + b*x^4)^2,x]","-\frac{3 (b c-a d)^2 (3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{13/4}}+\frac{3 (b c-a d)^2 (3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{13/4}}-\frac{3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{13/4}}+\frac{3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{13/4}}+\frac{d^2 x (3 b c-2 a d)}{b^3}+\frac{x (b c-a d)^3}{4 a b^3 \left(a+b x^4\right)}+\frac{d^3 x^5}{5 b^2}","-\frac{3 (b c-a d)^2 (3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{13/4}}+\frac{3 (b c-a d)^2 (3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{13/4}}-\frac{3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{13/4}}+\frac{3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{13/4}}+\frac{d^2 x (3 b c-2 a d)}{b^3}+\frac{x (b c-a d)^3}{4 a b^3 \left(a+b x^4\right)}+\frac{d^3 x^5}{5 b^2}",1,"(d^2*(3*b*c - 2*a*d)*x)/b^3 + (d^3*x^5)/(5*b^2) + ((b*c - a*d)^3*x)/(4*a*b^3*(a + b*x^4)) - (3*(b*c - a*d)^2*(b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(13/4)) + (3*(b*c - a*d)^2*(b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(13/4)) - (3*(b*c - a*d)^2*(b*c + 3*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(13/4)) + (3*(b*c - a*d)^2*(b*c + 3*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(13/4))","A",12,8,19,0.4211,1,"{390, 385, 211, 1165, 628, 1162, 617, 204}"
169,1,291,0,0.3772912,"\int \frac{\left(c+d x^4\right)^2}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x^4)^2/(a + b*x^4)^2,x]","-\frac{(b c-a d) (5 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(b c-a d) (5 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{9/4}}-\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{9/4}}+\frac{x (b c-a d)^2}{4 a b^2 \left(a+b x^4\right)}+\frac{d^2 x}{b^2}","-\frac{(b c-a d) (5 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(b c-a d) (5 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{9/4}}-\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{9/4}}+\frac{x (b c-a d)^2}{4 a b^2 \left(a+b x^4\right)}+\frac{d^2 x}{b^2}",1,"(d^2*x)/b^2 + ((b*c - a*d)^2*x)/(4*a*b^2*(a + b*x^4)) - ((b*c - a*d)*(3*b*c + 5*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(9/4)) + ((b*c - a*d)*(3*b*c + 5*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(9/4)) - ((b*c - a*d)*(3*b*c + 5*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(9/4)) + ((b*c - a*d)*(3*b*c + 5*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(9/4))","A",12,8,19,0.4211,1,"{390, 385, 211, 1165, 628, 1162, 617, 204}"
170,1,245,0,0.1528376,"\int \frac{c+d x^4}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x^4)/(a + b*x^4)^2,x]","-\frac{(a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}-\frac{(a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{x (b c-a d)}{4 a b \left(a+b x^4\right)}","-\frac{(a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}-\frac{(a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{x (b c-a d)}{4 a b \left(a+b x^4\right)}",1,"((b*c - a*d)*x)/(4*a*b*(a + b*x^4)) - ((3*b*c + a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(5/4)) + ((3*b*c + a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(5/4)) - ((3*b*c + a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(5/4)) + ((3*b*c + a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(5/4))","A",10,7,17,0.4118,1,"{385, 211, 1165, 628, 1162, 617, 204}"
171,1,513,0,0.4282916,"\int \frac{1}{\left(a+b x^4\right)^2 \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^2*(c + d*x^4)),x]","-\frac{b^{3/4} (3 b c-7 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} (b c-a d)^2}+\frac{b^{3/4} (3 b c-7 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} (b c-a d)^2}-\frac{b^{3/4} (3 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^2}+\frac{b^{3/4} (3 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^2}-\frac{d^{7/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)^2}+\frac{d^{7/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)^2}-\frac{d^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} (b c-a d)^2}+\frac{d^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} (b c-a d)^2}+\frac{b x}{4 a \left(a+b x^4\right) (b c-a d)}","-\frac{b^{3/4} (3 b c-7 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} (b c-a d)^2}+\frac{b^{3/4} (3 b c-7 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} (b c-a d)^2}-\frac{b^{3/4} (3 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^2}+\frac{b^{3/4} (3 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^2}-\frac{d^{7/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)^2}+\frac{d^{7/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)^2}-\frac{d^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} (b c-a d)^2}+\frac{d^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} (b c-a d)^2}+\frac{b x}{4 a \left(a+b x^4\right) (b c-a d)}",1,"(b*x)/(4*a*(b*c - a*d)*(a + b*x^4)) - (b^(3/4)*(3*b*c - 7*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(b*c - a*d)^2) + (b^(3/4)*(3*b*c - 7*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(b*c - a*d)^2) - (d^(7/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*(b*c - a*d)^2) + (d^(7/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*(b*c - a*d)^2) - (b^(3/4)*(3*b*c - 7*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*(b*c - a*d)^2) + (b^(3/4)*(3*b*c - 7*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*(b*c - a*d)^2) - (d^(7/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*(b*c - a*d)^2) + (d^(7/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*(b*c - a*d)^2)","A",20,8,19,0.4211,1,"{414, 522, 211, 1165, 628, 1162, 617, 204}"
172,1,596,0,0.7386211,"\int \frac{1}{\left(a+b x^4\right)^2 \left(c+d x^4\right)^2} \, dx","Int[1/((a + b*x^4)^2*(c + d*x^4)^2),x]","-\frac{b^{7/4} (3 b c-11 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{7/4} (3 b c-11 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{b^{7/4} (3 b c-11 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{7/4} (3 b c-11 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{d^{7/4} (11 b c-3 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{d^{7/4} (11 b c-3 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} (b c-a d)^3}-\frac{d^{7/4} (11 b c-3 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{d^{7/4} (11 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{b x}{4 a \left(a+b x^4\right) \left(c+d x^4\right) (b c-a d)}+\frac{d x (a d+b c)}{4 a c \left(c+d x^4\right) (b c-a d)^2}","-\frac{b^{7/4} (3 b c-11 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{7/4} (3 b c-11 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{b^{7/4} (3 b c-11 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{7/4} (3 b c-11 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{d^{7/4} (11 b c-3 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{d^{7/4} (11 b c-3 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{16 \sqrt{2} c^{7/4} (b c-a d)^3}-\frac{d^{7/4} (11 b c-3 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{d^{7/4} (11 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{b x}{4 a \left(a+b x^4\right) \left(c+d x^4\right) (b c-a d)}+\frac{d x (a d+b c)}{4 a c \left(c+d x^4\right) (b c-a d)^2}",1,"(d*(b*c + a*d)*x)/(4*a*c*(b*c - a*d)^2*(c + d*x^4)) + (b*x)/(4*a*(b*c - a*d)*(a + b*x^4)*(c + d*x^4)) - (b^(7/4)*(3*b*c - 11*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) + (b^(7/4)*(3*b*c - 11*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) - (d^(7/4)*(11*b*c - 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(8*Sqrt[2]*c^(7/4)*(b*c - a*d)^3) + (d^(7/4)*(11*b*c - 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(8*Sqrt[2]*c^(7/4)*(b*c - a*d)^3) - (b^(7/4)*(3*b*c - 11*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) + (b^(7/4)*(3*b*c - 11*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) - (d^(7/4)*(11*b*c - 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(16*Sqrt[2]*c^(7/4)*(b*c - a*d)^3) + (d^(7/4)*(11*b*c - 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(16*Sqrt[2]*c^(7/4)*(b*c - a*d)^3)","A",21,9,19,0.4737,1,"{414, 527, 522, 211, 1165, 628, 1162, 617, 204}"
173,1,321,0,0.3828829,"\int \frac{\left(a-b x^4\right)^{5/2}}{c-d x^4} \, dx","Int[(a - b*x^4)^(5/2)/(c - d*x^4),x]","\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} \left(47 a^2 d^2-56 a b c d+21 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{21 d^3 \sqrt{a-b x^4}}-\frac{b x \sqrt{a-b x^4} (7 b c-13 a d)}{21 d^2}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d)^3 \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^3 \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d)^3 \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^3 \sqrt{a-b x^4}}+\frac{b x \left(a-b x^4\right)^{3/2}}{7 d}","\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} \left(47 a^2 d^2-56 a b c d+21 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{21 d^3 \sqrt{a-b x^4}}-\frac{b x \sqrt{a-b x^4} (7 b c-13 a d)}{21 d^2}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d)^3 \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^3 \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d)^3 \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^3 \sqrt{a-b x^4}}+\frac{b x \left(a-b x^4\right)^{3/2}}{7 d}",1,"-(b*(7*b*c - 13*a*d)*x*Sqrt[a - b*x^4])/(21*d^2) + (b*x*(a - b*x^4)^(3/2))/(7*d) + (a^(1/4)*b^(3/4)*(21*b^2*c^2 - 56*a*b*c*d + 47*a^2*d^2)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(21*d^3*Sqrt[a - b*x^4]) - (a^(1/4)*(b*c - a*d)^3*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*d^3*Sqrt[a - b*x^4]) - (a^(1/4)*(b*c - a*d)^3*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*d^3*Sqrt[a - b*x^4])","A",10,8,23,0.3478,1,"{416, 528, 523, 224, 221, 409, 1219, 1218}"
174,1,277,0,0.2622019,"\int \frac{\left(a-b x^4\right)^{3/2}}{c-d x^4} \, dx","Int[(a - b*x^4)^(3/2)/(c - d*x^4),x]","-\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} (3 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{3 d^2 \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^2 \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d)^2 \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^2 \sqrt{a-b x^4}}+\frac{b x \sqrt{a-b x^4}}{3 d}","-\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} (3 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{3 d^2 \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^2 \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d)^2 \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^2 \sqrt{a-b x^4}}+\frac{b x \sqrt{a-b x^4}}{3 d}",1,"(b*x*Sqrt[a - b*x^4])/(3*d) - (a^(1/4)*b^(3/4)*(3*b*c - 5*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(3*d^2*Sqrt[a - b*x^4]) + (a^(1/4)*(b*c - a*d)^2*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*d^2*Sqrt[a - b*x^4]) + (a^(1/4)*(b*c - a*d)^2*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*d^2*Sqrt[a - b*x^4])","A",9,7,23,0.3043,1,"{416, 523, 224, 221, 409, 1219, 1218}"
175,1,240,0,0.1634731,"\int \frac{\sqrt{a-b x^4}}{c-d x^4} \, dx","Int[Sqrt[a - b*x^4]/(c - d*x^4),x]","\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{d \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d \sqrt{a-b x^4}}","\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{d \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d \sqrt{a-b x^4}}",1,"(a^(1/4)*b^(3/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(d*Sqrt[a - b*x^4]) - (a^(1/4)*(b*c - a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*d*Sqrt[a - b*x^4]) - (a^(1/4)*(b*c - a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*d*Sqrt[a - b*x^4])","A",8,6,23,0.2609,1,"{406, 224, 221, 409, 1219, 1218}"
176,1,162,0,0.1149943,"\int \frac{1}{\sqrt{a-b x^4} \left(c-d x^4\right)} \, dx","Int[1/(Sqrt[a - b*x^4]*(c - d*x^4)),x]","\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4}}","\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4}}",1,"(a^(1/4)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*Sqrt[a - b*x^4]) + (a^(1/4)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*Sqrt[a - b*x^4])","A",5,3,23,0.1304,1,"{409, 1219, 1218}"
177,1,281,0,0.2222029,"\int \frac{1}{\left(a-b x^4\right)^{3/2} \left(c-d x^4\right)} \, dx","Int[1/((a - b*x^4)^(3/2)*(c - d*x^4)),x]","\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 a^{3/4} \sqrt{a-b x^4} (b c-a d)}+\frac{b x}{2 a \sqrt{a-b x^4} (b c-a d)}-\frac{\sqrt[4]{a} d \sqrt{1-\frac{b x^4}{a}} \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4} (b c-a d)}-\frac{\sqrt[4]{a} d \sqrt{1-\frac{b x^4}{a}} \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4} (b c-a d)}","\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 a^{3/4} \sqrt{a-b x^4} (b c-a d)}+\frac{b x}{2 a \sqrt{a-b x^4} (b c-a d)}-\frac{\sqrt[4]{a} d \sqrt{1-\frac{b x^4}{a}} \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4} (b c-a d)}-\frac{\sqrt[4]{a} d \sqrt{1-\frac{b x^4}{a}} \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4} (b c-a d)}",1,"(b*x)/(2*a*(b*c - a*d)*Sqrt[a - b*x^4]) + (b^(3/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*a^(3/4)*(b*c - a*d)*Sqrt[a - b*x^4]) - (a^(1/4)*d*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)*Sqrt[a - b*x^4]) - (a^(1/4)*d*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)*Sqrt[a - b*x^4])","A",9,7,23,0.3043,1,"{414, 523, 224, 221, 409, 1219, 1218}"
178,1,334,0,0.3997876,"\int \frac{1}{\left(a-b x^4\right)^{5/2} \left(c-d x^4\right)} \, dx","Int[1/((a - b*x^4)^(5/2)*(c - d*x^4)),x]","\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} (5 b c-11 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{12 a^{7/4} \sqrt{a-b x^4} (b c-a d)^2}+\frac{b x (5 b c-11 a d)}{12 a^2 \sqrt{a-b x^4} (b c-a d)^2}+\frac{\sqrt[4]{a} d^2 \sqrt{1-\frac{b x^4}{a}} \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4} (b c-a d)^2}+\frac{\sqrt[4]{a} d^2 \sqrt{1-\frac{b x^4}{a}} \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4} (b c-a d)^2}+\frac{b x}{6 a \left(a-b x^4\right)^{3/2} (b c-a d)}","\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} (5 b c-11 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{12 a^{7/4} \sqrt{a-b x^4} (b c-a d)^2}+\frac{b x (5 b c-11 a d)}{12 a^2 \sqrt{a-b x^4} (b c-a d)^2}+\frac{\sqrt[4]{a} d^2 \sqrt{1-\frac{b x^4}{a}} \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4} (b c-a d)^2}+\frac{\sqrt[4]{a} d^2 \sqrt{1-\frac{b x^4}{a}} \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c \sqrt{a-b x^4} (b c-a d)^2}+\frac{b x}{6 a \left(a-b x^4\right)^{3/2} (b c-a d)}",1,"(b*x)/(6*a*(b*c - a*d)*(a - b*x^4)^(3/2)) + (b*(5*b*c - 11*a*d)*x)/(12*a^2*(b*c - a*d)^2*Sqrt[a - b*x^4]) + (b^(3/4)*(5*b*c - 11*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(12*a^(7/4)*(b*c - a*d)^2*Sqrt[a - b*x^4]) + (a^(1/4)*d^2*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)^2*Sqrt[a - b*x^4]) + (a^(1/4)*d^2*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)^2*Sqrt[a - b*x^4])","A",10,8,23,0.3478,1,"{414, 527, 523, 224, 221, 409, 1219, 1218}"
179,1,926,0,1.6551103,"\int \frac{\left(a+b x^4\right)^{3/2}}{c+d x^4} \, dx","Int[(a + b*x^4)^(3/2)/(c + d*x^4),x]","\frac{\sqrt[4]{b} \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) (b c-a d)^2}{4 \sqrt[4]{a} \sqrt{-c} d^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\sqrt[4]{b} \left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) (b c-a d)^2}{4 \sqrt[4]{a} \sqrt{-c} d^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2 \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) (b c-a d)^2}{8 \sqrt[4]{a} \sqrt[4]{b} c d^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2 \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) (b c-a d)^2}{8 \sqrt[4]{a} \sqrt[4]{b} c d^2 (b c+a d) \sqrt{b x^4+a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right) (b c-a d)^{3/2}}{4 (-c)^{3/4} d^{7/4}}-\frac{(a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} d^{7/4}}-\frac{b^{3/4} (3 b c-5 a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 \sqrt[4]{a} d^2 \sqrt{b x^4+a}}+\frac{b x \sqrt{b x^4+a}}{3 d}","\frac{\sqrt[4]{b} \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) (b c-a d)^2}{4 \sqrt[4]{a} \sqrt{-c} d^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\sqrt[4]{b} \left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) (b c-a d)^2}{4 \sqrt[4]{a} \sqrt{-c} d^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2 \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) (b c-a d)^2}{8 \sqrt[4]{a} \sqrt[4]{b} c d^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2 \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) (b c-a d)^2}{8 \sqrt[4]{a} \sqrt[4]{b} c d^2 (b c+a d) \sqrt{b x^4+a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right) (b c-a d)^{3/2}}{4 (-c)^{3/4} d^{7/4}}-\frac{(a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} d^{7/4}}-\frac{b^{3/4} (3 b c-5 a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 \sqrt[4]{a} d^2 \sqrt{b x^4+a}}+\frac{b x \sqrt{b x^4+a}}{3 d}",1,"(b*x*Sqrt[a + b*x^4])/(3*d) - ((b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*d^(7/4)) - ((-(b*c) + a*d)^(3/2)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*d^(7/4)) - (b^(3/4)*(3*b*c - 5*a*d)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(6*a^(1/4)*d^2*Sqrt[a + b*x^4]) + (b^(1/4)*(Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])*(b*c - a*d)^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*Sqrt[-c]*d^2*(b*c + a*d)*Sqrt[a + b*x^4]) + (b^(1/4)*(Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])*(b*c - a*d)^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*Sqrt[-c]*d^2*(b*c + a*d)*Sqrt[a + b*x^4]) + ((Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2*(b*c - a*d)^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*d^2*(b*c + a*d)*Sqrt[a + b*x^4]) + ((Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2*(b*c - a*d)^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*d^2*(b*c + a*d)*Sqrt[a + b*x^4])","A",10,6,21,0.2857,1,"{416, 523, 220, 409, 1217, 1707}"
180,1,881,0,0.8798991,"\int \frac{\sqrt{a+b x^4}}{c+d x^4} \, dx","Int[Sqrt[a + b*x^4]/(c + d*x^4),x]","-\frac{(b c-a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{8 \sqrt[4]{a} \sqrt[4]{b} c d (b c+a d) \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} (b c-a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)}{4 \sqrt[4]{a} \sqrt{-c} d (b c+a d) \sqrt{b x^4+a}}+\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} d^{3/4}}-\frac{\sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} d^{3/4}}+\frac{b^{3/4} \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} d \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} \left(\sqrt{b}+\frac{\sqrt{a} \sqrt{d}}{\sqrt{-c}}\right) (b c-a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} d (b c+a d) \sqrt{b x^4+a}}-\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{b} c d (b c+a d) \sqrt{b x^4+a}}","-\frac{(b c-a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{8 \sqrt[4]{a} \sqrt[4]{b} c d (b c+a d) \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} (b c-a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)}{4 \sqrt[4]{a} \sqrt{-c} d (b c+a d) \sqrt{b x^4+a}}+\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} d^{3/4}}-\frac{\sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} d^{3/4}}+\frac{b^{3/4} \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} d \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} \left(\sqrt{b}+\frac{\sqrt{a} \sqrt{d}}{\sqrt{-c}}\right) (b c-a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} d (b c+a d) \sqrt{b x^4+a}}-\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{b} c d (b c+a d) \sqrt{b x^4+a}}",1,"(Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*d^(3/4)) - (Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*d^(3/4)) + (b^(3/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*d*Sqrt[a + b*x^4]) - (b^(1/4)*(Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])*(b*c - a*d)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*Sqrt[-c]*d*(b*c + a*d)*Sqrt[a + b*x^4]) - (b^(1/4)*(Sqrt[b] + (Sqrt[a]*Sqrt[d])/Sqrt[-c])*(b*c - a*d)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*d*(b*c + a*d)*Sqrt[a + b*x^4]) - ((Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*d*(b*c + a*d)*Sqrt[a + b*x^4]) - ((Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*d*(b*c + a*d)*Sqrt[a + b*x^4])","A",9,5,21,0.2381,1,"{406, 220, 409, 1217, 1707}"
181,1,742,0,0.6330173,"\int \frac{1}{\sqrt{a+b x^4} \left(c+d x^4\right)} \, dx","Int[1/(Sqrt[a + b*x^4]*(c + d*x^4)),x]","-\frac{\sqrt[4]{d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{a+b x^4}}\right)}{4 (-c)^{3/4} \sqrt{b c-a d}}-\frac{\sqrt[4]{d} \tan ^{-1}\left(\frac{x \sqrt{a d-b c}}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{a+b x^4}}\right)}{4 (-c)^{3/4} \sqrt{a d-b c}}+\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{-c}}+\sqrt{b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt{a+b x^4} (a d+b c)}+\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} \sqrt{-c} \sqrt{d}+\sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} c \sqrt{a+b x^4} (a d+b c)}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2 \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{b} c \sqrt{a+b x^4} (a d+b c)}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{-c}\right)^2 \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{b} c \sqrt{a+b x^4} (a d+b c)}","-\frac{\sqrt[4]{d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{a+b x^4}}\right)}{4 (-c)^{3/4} \sqrt{b c-a d}}-\frac{\sqrt[4]{d} \tan ^{-1}\left(\frac{x \sqrt{a d-b c}}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{a+b x^4}}\right)}{4 (-c)^{3/4} \sqrt{a d-b c}}+\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{-c}}+\sqrt{b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt{a+b x^4} (a d+b c)}+\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} \sqrt{-c} \sqrt{d}+\sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} c \sqrt{a+b x^4} (a d+b c)}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2 \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{b} c \sqrt{a+b x^4} (a d+b c)}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{-c}\right)^2 \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{b} c \sqrt{a+b x^4} (a d+b c)}",1,"-(d^(1/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*Sqrt[b*c - a*d]) - (d^(1/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*Sqrt[-(b*c) + a*d]) + (b^(1/4)*(Sqrt[b] + (Sqrt[a]*Sqrt[d])/Sqrt[-c])*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*(b*c + a*d)*Sqrt[a + b*x^4]) + (b^(1/4)*(Sqrt[b]*c + Sqrt[a]*Sqrt[-c]*Sqrt[d])*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c*(b*c + a*d)*Sqrt[a + b*x^4]) + ((Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*(b*c + a*d)*Sqrt[a + b*x^4]) + ((Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*(b*c + a*d)*Sqrt[a + b*x^4])","A",7,4,21,0.1905,1,"{409, 1217, 220, 1707}"
182,1,913,0,1.1319584,"\int \frac{1}{\left(a+b x^4\right)^{3/2} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(3/2)*(c + d*x^4)),x]","-\frac{d \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{8 \sqrt[4]{a} \sqrt[4]{b} c (b c-a d) (b c+a d) \sqrt{b x^4+a}}+\frac{d^{5/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} (b c-a d)^{3/2}}-\frac{d^{5/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} (a d-b c)^{3/2}}+\frac{b^{3/4} \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} (b c-a d) \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} \left(\sqrt{b}+\frac{\sqrt{a} \sqrt{d}}{\sqrt{-c}}\right) d \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} (b c-a d) (b c+a d) \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} \left(\sqrt{b} c+\sqrt{a} \sqrt{-c} \sqrt{d}\right) d \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} c \left(b^2 c^2-a^2 d^2\right) \sqrt{b x^4+a}}-\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2 d \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{b} c (b c-a d) (b c+a d) \sqrt{b x^4+a}}+\frac{b x}{2 a (b c-a d) \sqrt{b x^4+a}}","-\frac{d \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{8 \sqrt[4]{a} \sqrt[4]{b} c (b c-a d) (b c+a d) \sqrt{b x^4+a}}+\frac{d^{5/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} (b c-a d)^{3/2}}-\frac{d^{5/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right)}{4 (-c)^{3/4} (a d-b c)^{3/2}}+\frac{b^{3/4} \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} (b c-a d) \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} \left(\sqrt{b}+\frac{\sqrt{a} \sqrt{d}}{\sqrt{-c}}\right) d \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} (b c-a d) (b c+a d) \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} \left(\sqrt{b} c+\sqrt{a} \sqrt{-c} \sqrt{d}\right) d \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} c \left(b^2 c^2-a^2 d^2\right) \sqrt{b x^4+a}}-\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2 d \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{b} c (b c-a d) (b c+a d) \sqrt{b x^4+a}}+\frac{b x}{2 a (b c-a d) \sqrt{b x^4+a}}",1,"(b*x)/(2*a*(b*c - a*d)*Sqrt[a + b*x^4]) + (d^(5/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*(b*c - a*d)^(3/2)) - (d^(5/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*(-(b*c) + a*d)^(3/2)) + (b^(3/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*(b*c - a*d)*Sqrt[a + b*x^4]) - (b^(1/4)*(Sqrt[b] + (Sqrt[a]*Sqrt[d])/Sqrt[-c])*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[a + b*x^4]) - (b^(1/4)*(Sqrt[b]*c + Sqrt[a]*Sqrt[-c]*Sqrt[d])*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c*(b^2*c^2 - a^2*d^2)*Sqrt[a + b*x^4]) - ((Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*(b*c - a*d)*(b*c + a*d)*Sqrt[a + b*x^4]) - ((Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*(b*c - a*d)*(b*c + a*d)*Sqrt[a + b*x^4])","A",10,6,21,0.2857,1,"{414, 523, 220, 409, 1217, 1707}"
183,1,976,0,1.6825136,"\int \frac{1}{\left(a+b x^4\right)^{5/2} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(5/2)*(c + d*x^4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right) d^{9/4}}{4 (-c)^{3/4} (b c-a d)^{5/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right) d^{9/4}}{4 (-c)^{3/4} (a d-b c)^{5/2}}+\frac{\sqrt[4]{b} \left(\sqrt{b} c-\sqrt{a} \sqrt{-c} \sqrt{d}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) d^2}{4 \sqrt[4]{a} c (b c-a d)^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\sqrt[4]{b} \left(\sqrt{b} c+\sqrt{a} \sqrt{-c} \sqrt{d}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) d^2}{4 \sqrt[4]{a} c (b c-a d)^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2 \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) d^2}{8 \sqrt[4]{a} \sqrt[4]{b} c (b c-a d)^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2 \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) d^2}{8 \sqrt[4]{a} \sqrt[4]{b} c (b c-a d)^2 (b c+a d) \sqrt{b x^4+a}}+\frac{b^{3/4} (5 b c-11 a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{24 a^{9/4} (b c-a d)^2 \sqrt{b x^4+a}}+\frac{b (5 b c-11 a d) x}{12 a^2 (b c-a d)^2 \sqrt{b x^4+a}}+\frac{b x}{6 a (b c-a d) \left(b x^4+a\right)^{3/2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right) d^{9/4}}{4 (-c)^{3/4} (b c-a d)^{5/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-c} \sqrt[4]{d} \sqrt{b x^4+a}}\right) d^{9/4}}{4 (-c)^{3/4} (a d-b c)^{5/2}}+\frac{\sqrt[4]{b} \left(\sqrt{b} c-\sqrt{a} \sqrt{-c} \sqrt{d}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) d^2}{4 \sqrt[4]{a} c (b c-a d)^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\sqrt[4]{b} \left(\sqrt{b} c+\sqrt{a} \sqrt{-c} \sqrt{d}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) d^2}{4 \sqrt[4]{a} c (b c-a d)^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2 \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) d^2}{8 \sqrt[4]{a} \sqrt[4]{b} c (b c-a d)^2 (b c+a d) \sqrt{b x^4+a}}+\frac{\left(\sqrt{b} \sqrt{-c}-\sqrt{a} \sqrt{d}\right)^2 \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{-c}+\sqrt{a} \sqrt{d}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) d^2}{8 \sqrt[4]{a} \sqrt[4]{b} c (b c-a d)^2 (b c+a d) \sqrt{b x^4+a}}+\frac{b^{3/4} (5 b c-11 a d) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{24 a^{9/4} (b c-a d)^2 \sqrt{b x^4+a}}+\frac{b (5 b c-11 a d) x}{12 a^2 (b c-a d)^2 \sqrt{b x^4+a}}+\frac{b x}{6 a (b c-a d) \left(b x^4+a\right)^{3/2}}",1,"(b*x)/(6*a*(b*c - a*d)*(a + b*x^4)^(3/2)) + (b*(5*b*c - 11*a*d)*x)/(12*a^2*(b*c - a*d)^2*Sqrt[a + b*x^4]) - (d^(9/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*(b*c - a*d)^(5/2)) - (d^(9/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-c)^(1/4)*d^(1/4)*Sqrt[a + b*x^4])])/(4*(-c)^(3/4)*(-(b*c) + a*d)^(5/2)) + (b^(3/4)*(5*b*c - 11*a*d)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(24*a^(9/4)*(b*c - a*d)^2*Sqrt[a + b*x^4]) + (b^(1/4)*(Sqrt[b]*c - Sqrt[a]*Sqrt[-c]*Sqrt[d])*d^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c*(b*c - a*d)^2*(b*c + a*d)*Sqrt[a + b*x^4]) + (b^(1/4)*(Sqrt[b]*c + Sqrt[a]*Sqrt[-c]*Sqrt[d])*d^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c*(b*c - a*d)^2*(b*c + a*d)*Sqrt[a + b*x^4]) + ((Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2*d^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*(b*c - a*d)^2*(b*c + a*d)*Sqrt[a + b*x^4]) + ((Sqrt[b]*Sqrt[-c] - Sqrt[a]*Sqrt[d])^2*d^2*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[-c] + Sqrt[a]*Sqrt[d])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[-c]*Sqrt[d]), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*b^(1/4)*c*(b*c - a*d)^2*(b*c + a*d)*Sqrt[a + b*x^4])","A",11,7,21,0.3333,1,"{414, 527, 523, 220, 409, 1217, 1707}"
184,1,426,0,0.5356717,"\int \frac{\left(a-b x^4\right)^{7/2}}{\left(c-d x^4\right)^2} \, dx","Int[(a - b*x^4)^(7/2)/(c - d*x^4)^2,x]","-\frac{b x \sqrt{a-b x^4} \left(21 a^2 d^2-122 a b c d+77 b^2 c^2\right)}{84 c d^3}+\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} \left(349 a^2 b c d^2+21 a^3 d^3-553 a b^2 c^2 d+231 b^3 c^3\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{84 c d^4 \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (3 a d+11 b c) (b c-a d)^3 \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^4 \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (3 a d+11 b c) (b c-a d)^3 \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^4 \sqrt{a-b x^4}}+\frac{b x \left(a-b x^4\right)^{3/2} (11 b c-7 a d)}{28 c d^2}-\frac{x \left(a-b x^4\right)^{5/2} (b c-a d)}{4 c d \left(c-d x^4\right)}","-\frac{b x \sqrt{a-b x^4} \left(21 a^2 d^2-122 a b c d+77 b^2 c^2\right)}{84 c d^3}+\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} \left(349 a^2 b c d^2+21 a^3 d^3-553 a b^2 c^2 d+231 b^3 c^3\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{84 c d^4 \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (3 a d+11 b c) (b c-a d)^3 \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^4 \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (3 a d+11 b c) (b c-a d)^3 \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^4 \sqrt{a-b x^4}}+\frac{b x \left(a-b x^4\right)^{3/2} (11 b c-7 a d)}{28 c d^2}-\frac{x \left(a-b x^4\right)^{5/2} (b c-a d)}{4 c d \left(c-d x^4\right)}",1,"-(b*(77*b^2*c^2 - 122*a*b*c*d + 21*a^2*d^2)*x*Sqrt[a - b*x^4])/(84*c*d^3) + (b*(11*b*c - 7*a*d)*x*(a - b*x^4)^(3/2))/(28*c*d^2) - ((b*c - a*d)*x*(a - b*x^4)^(5/2))/(4*c*d*(c - d*x^4)) + (a^(1/4)*b^(3/4)*(231*b^3*c^3 - 553*a*b^2*c^2*d + 349*a^2*b*c*d^2 + 21*a^3*d^3)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(84*c*d^4*Sqrt[a - b*x^4]) - (a^(1/4)*(b*c - a*d)^3*(11*b*c + 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*d^4*Sqrt[a - b*x^4]) - (a^(1/4)*(b*c - a*d)^3*(11*b*c + 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*d^4*Sqrt[a - b*x^4])","A",11,8,23,0.3478,1,"{413, 528, 523, 224, 221, 409, 1219, 1218}"
185,1,365,0,0.4045633,"\int \frac{\left(a-b x^4\right)^{5/2}}{\left(c-d x^4\right)^2} \, dx","Int[(a - b*x^4)^(5/2)/(c - d*x^4)^2,x]","-\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} \left(-3 a^2 d^2-26 a b c d+21 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{12 c d^3 \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (3 a d+7 b c) (b c-a d)^2 \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^3 \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (3 a d+7 b c) (b c-a d)^2 \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^3 \sqrt{a-b x^4}}+\frac{b x \sqrt{a-b x^4} (7 b c-3 a d)}{12 c d^2}-\frac{x \left(a-b x^4\right)^{3/2} (b c-a d)}{4 c d \left(c-d x^4\right)}","-\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} \left(-3 a^2 d^2-26 a b c d+21 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{12 c d^3 \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (3 a d+7 b c) (b c-a d)^2 \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^3 \sqrt{a-b x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (3 a d+7 b c) (b c-a d)^2 \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^3 \sqrt{a-b x^4}}+\frac{b x \sqrt{a-b x^4} (7 b c-3 a d)}{12 c d^2}-\frac{x \left(a-b x^4\right)^{3/2} (b c-a d)}{4 c d \left(c-d x^4\right)}",1,"(b*(7*b*c - 3*a*d)*x*Sqrt[a - b*x^4])/(12*c*d^2) - ((b*c - a*d)*x*(a - b*x^4)^(3/2))/(4*c*d*(c - d*x^4)) - (a^(1/4)*b^(3/4)*(21*b^2*c^2 - 26*a*b*c*d - 3*a^2*d^2)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(12*c*d^3*Sqrt[a - b*x^4]) + (a^(1/4)*(b*c - a*d)^2*(7*b*c + 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*d^3*Sqrt[a - b*x^4]) + (a^(1/4)*(b*c - a*d)^2*(7*b*c + 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*d^3*Sqrt[a - b*x^4])","A",10,8,23,0.3478,1,"{413, 528, 523, 224, 221, 409, 1219, 1218}"
186,1,309,0,0.2772408,"\int \frac{\left(a-b x^4\right)^{3/2}}{\left(c-d x^4\right)^2} \, dx","Int[(a - b*x^4)^(3/2)/(c - d*x^4)^2,x]","\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} (a d+3 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{4 c d^2 \sqrt{a-b x^4}}-\frac{3 \sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d) (a d+b c) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^2 \sqrt{a-b x^4}}-\frac{3 \sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d) (a d+b c) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^2 \sqrt{a-b x^4}}-\frac{x \sqrt{a-b x^4} (b c-a d)}{4 c d \left(c-d x^4\right)}","\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} (a d+3 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{4 c d^2 \sqrt{a-b x^4}}-\frac{3 \sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d) (a d+b c) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^2 \sqrt{a-b x^4}}-\frac{3 \sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-a d) (a d+b c) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^2 \sqrt{a-b x^4}}-\frac{x \sqrt{a-b x^4} (b c-a d)}{4 c d \left(c-d x^4\right)}",1,"-((b*c - a*d)*x*Sqrt[a - b*x^4])/(4*c*d*(c - d*x^4)) + (a^(1/4)*b^(3/4)*(3*b*c + a*d)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(4*c*d^2*Sqrt[a - b*x^4]) - (3*a^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*d^2*Sqrt[a - b*x^4]) - (3*a^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*d^2*Sqrt[a - b*x^4])","A",9,7,23,0.3043,1,"{413, 523, 224, 221, 409, 1219, 1218}"
187,1,276,0,0.214877,"\int \frac{\sqrt{a-b x^4}}{\left(c-d x^4\right)^2} \, dx","Int[Sqrt[a - b*x^4]/(c - d*x^4)^2,x]","\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{4 c d \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-3 a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-3 a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d \sqrt{a-b x^4}}+\frac{x \sqrt{a-b x^4}}{4 c \left(c-d x^4\right)}","\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{4 c d \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-3 a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d \sqrt{a-b x^4}}-\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (b c-3 a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d \sqrt{a-b x^4}}+\frac{x \sqrt{a-b x^4}}{4 c \left(c-d x^4\right)}",1,"(x*Sqrt[a - b*x^4])/(4*c*(c - d*x^4)) + (a^(1/4)*b^(3/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(4*c*d*Sqrt[a - b*x^4]) - (a^(1/4)*(b*c - 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*d*Sqrt[a - b*x^4]) - (a^(1/4)*(b*c - 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*d*Sqrt[a - b*x^4])","A",9,7,23,0.3043,1,"{412, 523, 224, 221, 409, 1219, 1218}"
188,1,310,0,0.247204,"\int \frac{1}{\sqrt{a-b x^4} \left(c-d x^4\right)^2} \, dx","Int[1/(Sqrt[a - b*x^4]*(c - d*x^4)^2),x]","-\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{4 c \sqrt{a-b x^4} (b c-a d)}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (5 b c-3 a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (5 b c-3 a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)}-\frac{d x \sqrt{a-b x^4}}{4 c \left(c-d x^4\right) (b c-a d)}","-\frac{\sqrt[4]{a} b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{4 c \sqrt{a-b x^4} (b c-a d)}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (5 b c-3 a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)}+\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} (5 b c-3 a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)}-\frac{d x \sqrt{a-b x^4}}{4 c \left(c-d x^4\right) (b c-a d)}",1,"-(d*x*Sqrt[a - b*x^4])/(4*c*(b*c - a*d)*(c - d*x^4)) - (a^(1/4)*b^(3/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(4*c*(b*c - a*d)*Sqrt[a - b*x^4]) + (a^(1/4)*(5*b*c - 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)*Sqrt[a - b*x^4]) + (a^(1/4)*(5*b*c - 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)*Sqrt[a - b*x^4])","A",9,7,23,0.3043,1,"{414, 523, 224, 221, 409, 1219, 1218}"
189,1,362,0,0.4042303,"\int \frac{1}{\left(a-b x^4\right)^{3/2} \left(c-d x^4\right)^2} \, dx","Int[1/((a - b*x^4)^(3/2)*(c - d*x^4)^2),x]","\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} (a d+2 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{4 a^{3/4} c \sqrt{a-b x^4} (b c-a d)^2}-\frac{3 \sqrt[4]{a} d \sqrt{1-\frac{b x^4}{a}} (3 b c-a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)^2}-\frac{3 \sqrt[4]{a} d \sqrt{1-\frac{b x^4}{a}} (3 b c-a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)^2}+\frac{b x (a d+2 b c)}{4 a c \sqrt{a-b x^4} (b c-a d)^2}-\frac{d x}{4 c \sqrt{a-b x^4} \left(c-d x^4\right) (b c-a d)}","\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} (a d+2 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{4 a^{3/4} c \sqrt{a-b x^4} (b c-a d)^2}-\frac{3 \sqrt[4]{a} d \sqrt{1-\frac{b x^4}{a}} (3 b c-a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)^2}-\frac{3 \sqrt[4]{a} d \sqrt{1-\frac{b x^4}{a}} (3 b c-a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)^2}+\frac{b x (a d+2 b c)}{4 a c \sqrt{a-b x^4} (b c-a d)^2}-\frac{d x}{4 c \sqrt{a-b x^4} \left(c-d x^4\right) (b c-a d)}",1,"(b*(2*b*c + a*d)*x)/(4*a*c*(b*c - a*d)^2*Sqrt[a - b*x^4]) - (d*x)/(4*c*(b*c - a*d)*Sqrt[a - b*x^4]*(c - d*x^4)) + (b^(3/4)*(2*b*c + a*d)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(4*a^(3/4)*c*(b*c - a*d)^2*Sqrt[a - b*x^4]) - (3*a^(1/4)*d*(3*b*c - a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)^2*Sqrt[a - b*x^4]) - (3*a^(1/4)*d*(3*b*c - a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)^2*Sqrt[a - b*x^4])","A",10,8,23,0.3478,1,"{414, 527, 523, 224, 221, 409, 1219, 1218}"
190,1,439,0,0.535515,"\int \frac{1}{\left(a-b x^4\right)^{5/2} \left(c-d x^4\right)^2} \, dx","Int[1/((a - b*x^4)^(5/2)*(c - d*x^4)^2),x]","\frac{b x \left(-3 a^2 d^2-17 a b c d+5 b^2 c^2\right)}{12 a^2 c \sqrt{a-b x^4} (b c-a d)^3}+\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} \left(-3 a^2 d^2-17 a b c d+5 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{12 a^{7/4} c \sqrt{a-b x^4} (b c-a d)^3}+\frac{\sqrt[4]{a} d^2 \sqrt{1-\frac{b x^4}{a}} (13 b c-3 a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)^3}+\frac{\sqrt[4]{a} d^2 \sqrt{1-\frac{b x^4}{a}} (13 b c-3 a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)^3}-\frac{d x}{4 c \left(a-b x^4\right)^{3/2} \left(c-d x^4\right) (b c-a d)}+\frac{b x (3 a d+2 b c)}{12 a c \left(a-b x^4\right)^{3/2} (b c-a d)^2}","\frac{b x \left(-3 a^2 d^2-17 a b c d+5 b^2 c^2\right)}{12 a^2 c \sqrt{a-b x^4} (b c-a d)^3}+\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} \left(-3 a^2 d^2-17 a b c d+5 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{12 a^{7/4} c \sqrt{a-b x^4} (b c-a d)^3}+\frac{\sqrt[4]{a} d^2 \sqrt{1-\frac{b x^4}{a}} (13 b c-3 a d) \Pi \left(-\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)^3}+\frac{\sqrt[4]{a} d^2 \sqrt{1-\frac{b x^4}{a}} (13 b c-3 a d) \Pi \left(\frac{\sqrt{a} \sqrt{d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 \sqrt{a-b x^4} (b c-a d)^3}-\frac{d x}{4 c \left(a-b x^4\right)^{3/2} \left(c-d x^4\right) (b c-a d)}+\frac{b x (3 a d+2 b c)}{12 a c \left(a-b x^4\right)^{3/2} (b c-a d)^2}",1,"(b*(2*b*c + 3*a*d)*x)/(12*a*c*(b*c - a*d)^2*(a - b*x^4)^(3/2)) + (b*(5*b^2*c^2 - 17*a*b*c*d - 3*a^2*d^2)*x)/(12*a^2*c*(b*c - a*d)^3*Sqrt[a - b*x^4]) - (d*x)/(4*c*(b*c - a*d)*(a - b*x^4)^(3/2)*(c - d*x^4)) + (b^(3/4)*(5*b^2*c^2 - 17*a*b*c*d - 3*a^2*d^2)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(12*a^(7/4)*c*(b*c - a*d)^3*Sqrt[a - b*x^4]) + (a^(1/4)*d^2*(13*b*c - 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[-((Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)^3*Sqrt[a - b*x^4]) + (a^(1/4)*d^2*(13*b*c - 3*a*d)*Sqrt[1 - (b*x^4)/a]*EllipticPi[(Sqrt[a]*Sqrt[d])/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)^3*Sqrt[a - b*x^4])","A",11,8,23,0.3478,1,"{414, 527, 523, 224, 221, 409, 1219, 1218}"
191,1,103,0,0.0557869,"\int \frac{\sqrt{a+b x^4}}{a c-b c x^4} \, dx","Int[Sqrt[a + b*x^4]/(a*c - b*c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a+b x^4}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} c}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a+b x^4}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} c}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a+b x^4}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} c}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a+b x^4}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b} c}",1,"ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[a + b*x^4]]/(2*Sqrt[2]*a^(1/4)*b^(1/4)*c) + ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[a + b*x^4]]/(2*Sqrt[2]*a^(1/4)*b^(1/4)*c)","A",4,4,25,0.1600,1,"{404, 212, 206, 203}"
192,1,116,0,0.0234927,"\int \frac{\sqrt{a-b x^4}}{a c+b c x^4} \, dx","Int[Sqrt[a - b*x^4]/(a*c + b*c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x \left(\sqrt{a}+\sqrt{b} x^2\right)}{\sqrt[4]{a} \sqrt{a-b x^4}}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} c}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x \left(\sqrt{a}-\sqrt{b} x^2\right)}{\sqrt[4]{a} \sqrt{a-b x^4}}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} c}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x \left(\sqrt{a}+\sqrt{b} x^2\right)}{\sqrt[4]{a} \sqrt{a-b x^4}}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} c}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x \left(\sqrt{a}-\sqrt{b} x^2\right)}{\sqrt[4]{a} \sqrt{a-b x^4}}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} c}",1,"ArcTan[(b^(1/4)*x*(Sqrt[a] + Sqrt[b]*x^2))/(a^(1/4)*Sqrt[a - b*x^4])]/(2*a^(1/4)*b^(1/4)*c) + ArcTanh[(b^(1/4)*x*(Sqrt[a] - Sqrt[b]*x^2))/(a^(1/4)*Sqrt[a - b*x^4])]/(2*a^(1/4)*b^(1/4)*c)","A",1,1,25,0.04000,1,"{405}"
193,1,211,0,0.2246813,"\int \frac{\left(a+b x^4\right)^{7/4}}{c+d x^4} \, dx","Int[(a + b*x^4)^(7/4)/(c + d*x^4),x]","-\frac{b^{3/4} (4 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 d^2}-\frac{b^{3/4} (4 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 d^2}+\frac{(b c-a d)^{7/4} \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} d^2}+\frac{(b c-a d)^{7/4} \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} d^2}+\frac{b x \left(a+b x^4\right)^{3/4}}{4 d}","-\frac{b^{3/4} (4 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 d^2}-\frac{b^{3/4} (4 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 d^2}+\frac{(b c-a d)^{7/4} \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} d^2}+\frac{(b c-a d)^{7/4} \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} d^2}+\frac{b x \left(a+b x^4\right)^{3/4}}{4 d}",1,"(b*x*(a + b*x^4)^(3/4))/(4*d) - (b^(3/4)*(4*b*c - 7*a*d)*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*d^2) + ((b*c - a*d)^(7/4)*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*d^2) - (b^(3/4)*(4*b*c - 7*a*d)*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*d^2) + ((b*c - a*d)^(7/4)*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*d^2)","A",10,9,21,0.4286,1,"{416, 530, 240, 212, 206, 203, 377, 208, 205}"
194,1,173,0,0.1031244,"\int \frac{\left(a+b x^4\right)^{3/4}}{c+d x^4} \, dx","Int[(a + b*x^4)^(3/4)/(c + d*x^4),x]","\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 d}+\frac{b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 d}-\frac{(b c-a d)^{3/4} \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} d}-\frac{(b c-a d)^{3/4} \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} d}","\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 d}+\frac{b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 d}-\frac{(b c-a d)^{3/4} \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} d}-\frac{(b c-a d)^{3/4} \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} d}",1,"(b^(3/4)*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(2*d) - ((b*c - a*d)^(3/4)*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*d) + (b^(3/4)*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(2*d) - ((b*c - a*d)^(3/4)*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*d)","A",9,8,21,0.3810,1,"{408, 240, 212, 206, 203, 377, 208, 205}"
195,1,105,0,0.0569827,"\int \frac{1}{\sqrt[4]{a+b x^4} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(1/4)*(c + d*x^4)),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} \sqrt[4]{b c-a d}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} \sqrt[4]{b c-a d}}","\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} \sqrt[4]{b c-a d}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} \sqrt[4]{b c-a d}}",1,"ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))]/(2*c^(3/4)*(b*c - a*d)^(1/4)) + ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))]/(2*c^(3/4)*(b*c - a*d)^(1/4))","A",4,4,21,0.1905,1,"{377, 212, 208, 205}"
196,1,134,0,0.0961695,"\int \frac{1}{\left(a+b x^4\right)^{5/4} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(5/4)*(c + d*x^4)),x]","-\frac{d \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{5/4}}-\frac{d \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{5/4}}+\frac{b x}{a \sqrt[4]{a+b x^4} (b c-a d)}","-\frac{d \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{5/4}}-\frac{d \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{5/4}}+\frac{b x}{a \sqrt[4]{a+b x^4} (b c-a d)}",1,"(b*x)/(a*(b*c - a*d)*(a + b*x^4)^(1/4)) - (d*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*(b*c - a*d)^(5/4)) - (d*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*(b*c - a*d)^(5/4))","A",5,5,21,0.2381,1,"{382, 377, 212, 208, 205}"
197,1,180,0,0.2025675,"\int \frac{1}{\left(a+b x^4\right)^{9/4} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(9/4)*(c + d*x^4)),x]","\frac{b x (4 b c-9 a d)}{5 a^2 \sqrt[4]{a+b x^4} (b c-a d)^2}+\frac{d^2 \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{9/4}}+\frac{d^2 \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{9/4}}+\frac{b x}{5 a \left(a+b x^4\right)^{5/4} (b c-a d)}","\frac{b x (4 b c-9 a d)}{5 a^2 \sqrt[4]{a+b x^4} (b c-a d)^2}+\frac{d^2 \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{9/4}}+\frac{d^2 \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{9/4}}+\frac{b x}{5 a \left(a+b x^4\right)^{5/4} (b c-a d)}",1,"(b*x)/(5*a*(b*c - a*d)*(a + b*x^4)^(5/4)) + (b*(4*b*c - 9*a*d)*x)/(5*a^2*(b*c - a*d)^2*(a + b*x^4)^(1/4)) + (d^2*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*(b*c - a*d)^(9/4)) + (d^2*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*(b*c - a*d)^(9/4))","A",7,7,21,0.3333,1,"{414, 527, 12, 377, 212, 208, 205}"
198,1,233,0,0.2949588,"\int \frac{1}{\left(a+b x^4\right)^{13/4} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(13/4)*(c + d*x^4)),x]","\frac{b x \left(113 a^2 d^2-100 a b c d+32 b^2 c^2\right)}{45 a^3 \sqrt[4]{a+b x^4} (b c-a d)^3}+\frac{b x (8 b c-17 a d)}{45 a^2 \left(a+b x^4\right)^{5/4} (b c-a d)^2}-\frac{d^3 \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{13/4}}-\frac{d^3 \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{13/4}}+\frac{b x}{9 a \left(a+b x^4\right)^{9/4} (b c-a d)}","\frac{b x \left(113 a^2 d^2-100 a b c d+32 b^2 c^2\right)}{45 a^3 \sqrt[4]{a+b x^4} (b c-a d)^3}+\frac{b x (8 b c-17 a d)}{45 a^2 \left(a+b x^4\right)^{5/4} (b c-a d)^2}-\frac{d^3 \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{13/4}}-\frac{d^3 \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{2 c^{3/4} (b c-a d)^{13/4}}+\frac{b x}{9 a \left(a+b x^4\right)^{9/4} (b c-a d)}",1,"(b*x)/(9*a*(b*c - a*d)*(a + b*x^4)^(9/4)) + (b*(8*b*c - 17*a*d)*x)/(45*a^2*(b*c - a*d)^2*(a + b*x^4)^(5/4)) + (b*(32*b^2*c^2 - 100*a*b*c*d + 113*a^2*d^2)*x)/(45*a^3*(b*c - a*d)^3*(a + b*x^4)^(1/4)) - (d^3*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*(b*c - a*d)^(13/4)) - (d^3*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(2*c^(3/4)*(b*c - a*d)^(13/4))","A",8,7,21,0.3333,1,"{414, 527, 12, 377, 212, 208, 205}"
199,1,316,0,0.3380131,"\int \frac{\left(a+b x^4\right)^{9/4}}{c+d x^4} \, dx","Int[(a + b*x^4)^(9/4)/(c + d*x^4),x]","\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} (6 b c-11 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 d^2 \left(a+b x^4\right)^{3/4}}-\frac{b x \sqrt[4]{a+b x^4} (6 b c-11 a d)}{12 d^2}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^2}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d)^2 \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^2}+\frac{b x \left(a+b x^4\right)^{5/4}}{6 d}","\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} (6 b c-11 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 d^2 \left(a+b x^4\right)^{3/4}}-\frac{b x \sqrt[4]{a+b x^4} (6 b c-11 a d)}{12 d^2}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^2}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d)^2 \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d^2}+\frac{b x \left(a+b x^4\right)^{5/4}}{6 d}",1,"-(b*(6*b*c - 11*a*d)*x*(a + b*x^4)^(1/4))/(12*d^2) + (b*x*(a + b*x^4)^(5/4))/(6*d) + (Sqrt[a]*b^(3/2)*(6*b*c - 11*a*d)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*d^2*(a + b*x^4)^(3/4)) + ((b*c - a*d)^2*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*d^2) + ((b*c - a*d)^2*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*d^2)","A",11,10,21,0.4762,1,"{416, 528, 529, 237, 335, 275, 231, 407, 409, 1218}"
200,1,274,0,0.1556686,"\int \frac{\left(a+b x^4\right)^{5/4}}{c+d x^4} \, dx","Int[(a + b*x^4)^(5/4)/(c + d*x^4),x]","-\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 d \left(a+b x^4\right)^{3/4}}-\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d}-\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d}+\frac{b x \sqrt[4]{a+b x^4}}{2 d}","-\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 d \left(a+b x^4\right)^{3/4}}-\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d}-\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c d}+\frac{b x \sqrt[4]{a+b x^4}}{2 d}",1,"(b*x*(a + b*x^4)^(1/4))/(2*d) - (Sqrt[a]*b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*d*(a + b*x^4)^(3/4)) - ((b*c - a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*d) - ((b*c - a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*d)","A",10,9,21,0.4286,1,"{408, 195, 237, 335, 275, 231, 407, 409, 1218}"
201,1,166,0,0.0885933,"\int \frac{\sqrt[4]{a+b x^4}}{c+d x^4} \, dx","Int[(a + b*x^4)^(1/4)/(c + d*x^4),x]","\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c}","\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c}",1,"(Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c) + (Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c)","A",4,3,21,0.1429,1,"{407, 409, 1218}"
202,1,259,0,0.1541643,"\int \frac{1}{\left(a+b x^4\right)^{3/4} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(3/4)*(c + d*x^4)),x]","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a+b x^4\right)^{3/4} (b c-a d)}-\frac{d \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)}-\frac{d \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)}","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a+b x^4\right)^{3/4} (b c-a d)}-\frac{d \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)}-\frac{d \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)}",1,"-((b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[a]*(b*c - a*d)*(a + b*x^4)^(3/4))) - (d*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)) - (d*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d))","A",9,8,21,0.3810,1,"{410, 237, 335, 275, 231, 407, 409, 1218}"
203,1,304,0,0.238478,"\int \frac{1}{\left(a+b x^4\right)^{7/4} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(7/4)*(c + d*x^4)),x]","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} (2 b c-5 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \left(a+b x^4\right)^{3/4} (b c-a d)^2}+\frac{d^2 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)^2}+\frac{d^2 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)^2}+\frac{b x}{3 a \left(a+b x^4\right)^{3/4} (b c-a d)}","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} (2 b c-5 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \left(a+b x^4\right)^{3/4} (b c-a d)^2}+\frac{d^2 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)^2}+\frac{d^2 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)^2}+\frac{b x}{3 a \left(a+b x^4\right)^{3/4} (b c-a d)}",1,"(b*x)/(3*a*(b*c - a*d)*(a + b*x^4)^(3/4)) - (b^(3/2)*(2*b*c - 5*a*d)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*a^(3/2)*(b*c - a*d)^2*(a + b*x^4)^(3/4)) + (d^2*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)^2) + (d^2*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)^2)","A",10,9,21,0.4286,1,"{414, 529, 237, 335, 275, 231, 407, 409, 1218}"
204,1,357,0,0.4009355,"\int \frac{1}{\left(a+b x^4\right)^{11/4} \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)^(11/4)*(c + d*x^4)),x]","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} \left(47 a^2 d^2-38 a b c d+12 b^2 c^2\right) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 a^{5/2} \left(a+b x^4\right)^{3/4} (b c-a d)^3}+\frac{b x (6 b c-13 a d)}{21 a^2 \left(a+b x^4\right)^{3/4} (b c-a d)^2}-\frac{d^3 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)^3}-\frac{d^3 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)^3}+\frac{b x}{7 a \left(a+b x^4\right)^{7/4} (b c-a d)}","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} \left(47 a^2 d^2-38 a b c d+12 b^2 c^2\right) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 a^{5/2} \left(a+b x^4\right)^{3/4} (b c-a d)^3}+\frac{b x (6 b c-13 a d)}{21 a^2 \left(a+b x^4\right)^{3/4} (b c-a d)^2}-\frac{d^3 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)^3}-\frac{d^3 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{2 \sqrt[4]{b} c (b c-a d)^3}+\frac{b x}{7 a \left(a+b x^4\right)^{7/4} (b c-a d)}",1,"(b*x)/(7*a*(b*c - a*d)*(a + b*x^4)^(7/4)) + (b*(6*b*c - 13*a*d)*x)/(21*a^2*(b*c - a*d)^2*(a + b*x^4)^(3/4)) - (b^(3/2)*(12*b^2*c^2 - 38*a*b*c*d + 47*a^2*d^2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(21*a^(5/2)*(b*c - a*d)^3*(a + b*x^4)^(3/4)) - (d^3*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)^3) - (d^3*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(2*b^(1/4)*c*(b*c - a*d)^3)","A",11,10,21,0.4762,1,"{414, 527, 529, 237, 335, 275, 231, 407, 409, 1218}"
205,1,280,0,0.3589976,"\int \frac{\left(a+b x^4\right)^{11/4}}{\left(c+d x^4\right)^2} \, dx","Int[(a + b*x^4)^(11/4)/(c + d*x^4)^2,x]","-\frac{b^{7/4} (8 b c-11 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 d^3}-\frac{b^{7/4} (8 b c-11 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 d^3}+\frac{(b c-a d)^{7/4} (3 a d+8 b c) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} d^3}+\frac{(b c-a d)^{7/4} (3 a d+8 b c) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} d^3}+\frac{b x \left(a+b x^4\right)^{3/4} (2 b c-a d)}{4 c d^2}-\frac{x \left(a+b x^4\right)^{7/4} (b c-a d)}{4 c d \left(c+d x^4\right)}","-\frac{b^{7/4} (8 b c-11 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 d^3}-\frac{b^{7/4} (8 b c-11 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 d^3}+\frac{(b c-a d)^{7/4} (3 a d+8 b c) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} d^3}+\frac{(b c-a d)^{7/4} (3 a d+8 b c) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} d^3}+\frac{b x \left(a+b x^4\right)^{3/4} (2 b c-a d)}{4 c d^2}-\frac{x \left(a+b x^4\right)^{7/4} (b c-a d)}{4 c d \left(c+d x^4\right)}",1,"(b*(2*b*c - a*d)*x*(a + b*x^4)^(3/4))/(4*c*d^2) - ((b*c - a*d)*x*(a + b*x^4)^(7/4))/(4*c*d*(c + d*x^4)) - (b^(7/4)*(8*b*c - 11*a*d)*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*d^3) + ((b*c - a*d)^(7/4)*(8*b*c + 3*a*d)*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*d^3) - (b^(7/4)*(8*b*c - 11*a*d)*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*d^3) + ((b*c - a*d)^(7/4)*(8*b*c + 3*a*d)*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*d^3)","A",11,10,21,0.4762,1,"{413, 528, 530, 240, 212, 206, 203, 377, 208, 205}"
206,1,230,0,0.1753041,"\int \frac{\left(a+b x^4\right)^{7/4}}{\left(c+d x^4\right)^2} \, dx","Int[(a + b*x^4)^(7/4)/(c + d*x^4)^2,x]","\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 d^2}+\frac{b^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 d^2}-\frac{(b c-a d)^{3/4} (3 a d+4 b c) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} d^2}-\frac{(b c-a d)^{3/4} (3 a d+4 b c) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} d^2}-\frac{x \left(a+b x^4\right)^{3/4} (b c-a d)}{4 c d \left(c+d x^4\right)}","\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 d^2}+\frac{b^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 d^2}-\frac{(b c-a d)^{3/4} (3 a d+4 b c) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} d^2}-\frac{(b c-a d)^{3/4} (3 a d+4 b c) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} d^2}-\frac{x \left(a+b x^4\right)^{3/4} (b c-a d)}{4 c d \left(c+d x^4\right)}",1,"-((b*c - a*d)*x*(a + b*x^4)^(3/4))/(4*c*d*(c + d*x^4)) + (b^(7/4)*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(2*d^2) - ((b*c - a*d)^(3/4)*(4*b*c + 3*a*d)*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*d^2) + (b^(7/4)*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(2*d^2) - ((b*c - a*d)^(3/4)*(4*b*c + 3*a*d)*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*d^2)","A",10,9,21,0.4286,1,"{413, 530, 240, 212, 206, 203, 377, 208, 205}"
207,1,135,0,0.0762624,"\int \frac{\left(a+b x^4\right)^{3/4}}{\left(c+d x^4\right)^2} \, dx","Int[(a + b*x^4)^(3/4)/(c + d*x^4)^2,x]","\frac{3 a \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} \sqrt[4]{b c-a d}}+\frac{3 a \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} \sqrt[4]{b c-a d}}+\frac{x \left(a+b x^4\right)^{3/4}}{4 c \left(c+d x^4\right)}","\frac{3 a \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} \sqrt[4]{b c-a d}}+\frac{3 a \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} \sqrt[4]{b c-a d}}+\frac{x \left(a+b x^4\right)^{3/4}}{4 c \left(c+d x^4\right)}",1,"(x*(a + b*x^4)^(3/4))/(4*c*(c + d*x^4)) + (3*a*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*(b*c - a*d)^(1/4)) + (3*a*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*(b*c - a*d)^(1/4))","A",5,5,21,0.2381,1,"{378, 377, 212, 208, 205}"
208,1,162,0,0.1085148,"\int \frac{1}{\sqrt[4]{a+b x^4} \left(c+d x^4\right)^2} \, dx","Int[1/((a + b*x^4)^(1/4)*(c + d*x^4)^2),x]","\frac{(4 b c-3 a d) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{5/4}}+\frac{(4 b c-3 a d) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{5/4}}-\frac{d x \left(a+b x^4\right)^{3/4}}{4 c \left(c+d x^4\right) (b c-a d)}","\frac{(4 b c-3 a d) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{5/4}}+\frac{(4 b c-3 a d) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{5/4}}-\frac{d x \left(a+b x^4\right)^{3/4}}{4 c \left(c+d x^4\right) (b c-a d)}",1,"-(d*x*(a + b*x^4)^(3/4))/(4*c*(b*c - a*d)*(c + d*x^4)) + ((4*b*c - 3*a*d)*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*(b*c - a*d)^(5/4)) + ((4*b*c - 3*a*d)*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*(b*c - a*d)^(5/4))","A",5,5,21,0.2381,1,"{382, 377, 212, 208, 205}"
209,1,205,0,0.184153,"\int \frac{1}{\left(a+b x^4\right)^{5/4} \left(c+d x^4\right)^2} \, dx","Int[1/((a + b*x^4)^(5/4)*(c + d*x^4)^2),x]","-\frac{d (8 b c-3 a d) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{9/4}}-\frac{d (8 b c-3 a d) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{9/4}}+\frac{b x (a d+4 b c)}{4 a c \sqrt[4]{a+b x^4} (b c-a d)^2}-\frac{d x}{4 c \sqrt[4]{a+b x^4} \left(c+d x^4\right) (b c-a d)}","-\frac{d (8 b c-3 a d) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{9/4}}-\frac{d (8 b c-3 a d) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{9/4}}+\frac{b x (a d+4 b c)}{4 a c \sqrt[4]{a+b x^4} (b c-a d)^2}-\frac{d x}{4 c \sqrt[4]{a+b x^4} \left(c+d x^4\right) (b c-a d)}",1,"(b*(4*b*c + a*d)*x)/(4*a*c*(b*c - a*d)^2*(a + b*x^4)^(1/4)) - (d*x)/(4*c*(b*c - a*d)*(a + b*x^4)^(1/4)*(c + d*x^4)) - (d*(8*b*c - 3*a*d)*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*(b*c - a*d)^(9/4)) - (d*(8*b*c - 3*a*d)*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*(b*c - a*d)^(9/4))","A",7,7,21,0.3333,1,"{414, 527, 12, 377, 212, 208, 205}"
210,1,266,0,0.2928554,"\int \frac{1}{\left(a+b x^4\right)^{9/4} \left(c+d x^4\right)^2} \, dx","Int[1/((a + b*x^4)^(9/4)*(c + d*x^4)^2),x]","\frac{b x \left(-5 a^2 d^2-56 a b c d+16 b^2 c^2\right)}{20 a^2 c \sqrt[4]{a+b x^4} (b c-a d)^3}+\frac{3 d^2 (4 b c-a d) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{13/4}}+\frac{3 d^2 (4 b c-a d) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{13/4}}-\frac{d x}{4 c \left(a+b x^4\right)^{5/4} \left(c+d x^4\right) (b c-a d)}+\frac{b x (5 a d+4 b c)}{20 a c \left(a+b x^4\right)^{5/4} (b c-a d)^2}","\frac{b x \left(-5 a^2 d^2-56 a b c d+16 b^2 c^2\right)}{20 a^2 c \sqrt[4]{a+b x^4} (b c-a d)^3}+\frac{3 d^2 (4 b c-a d) \tan ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{13/4}}+\frac{3 d^2 (4 b c-a d) \tanh ^{-1}\left(\frac{x \sqrt[4]{b c-a d}}{\sqrt[4]{c} \sqrt[4]{a+b x^4}}\right)}{8 c^{7/4} (b c-a d)^{13/4}}-\frac{d x}{4 c \left(a+b x^4\right)^{5/4} \left(c+d x^4\right) (b c-a d)}+\frac{b x (5 a d+4 b c)}{20 a c \left(a+b x^4\right)^{5/4} (b c-a d)^2}",1,"(b*(4*b*c + 5*a*d)*x)/(20*a*c*(b*c - a*d)^2*(a + b*x^4)^(5/4)) + (b*(16*b^2*c^2 - 56*a*b*c*d - 5*a^2*d^2)*x)/(20*a^2*c*(b*c - a*d)^3*(a + b*x^4)^(1/4)) - (d*x)/(4*c*(b*c - a*d)*(a + b*x^4)^(5/4)*(c + d*x^4)) + (3*d^2*(4*b*c - a*d)*ArcTan[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*(b*c - a*d)^(13/4)) + (3*d^2*(4*b*c - a*d)*ArcTanh[((b*c - a*d)^(1/4)*x)/(c^(1/4)*(a + b*x^4)^(1/4))])/(8*c^(7/4)*(b*c - a*d)^(13/4))","A",8,7,21,0.3333,1,"{414, 527, 12, 377, 212, 208, 205}"
211,1,353,0,0.3479311,"\int \frac{\left(a+b x^4\right)^{9/4}}{\left(c+d x^4\right)^2} \, dx","Int[(a + b*x^4)^(9/4)/(c + d*x^4)^2,x]","-\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} (3 b c-a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 c d^2 \left(a+b x^4\right)^{3/4}}-\frac{3 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d) (a d+2 b c) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^2}-\frac{3 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d) (a d+2 b c) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^2}+\frac{b x \sqrt[4]{a+b x^4} (3 b c-a d)}{4 c d^2}-\frac{x \left(a+b x^4\right)^{5/4} (b c-a d)}{4 c d \left(c+d x^4\right)}","-\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} (3 b c-a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 c d^2 \left(a+b x^4\right)^{3/4}}-\frac{3 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d) (a d+2 b c) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^2}-\frac{3 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (b c-a d) (a d+2 b c) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d^2}+\frac{b x \sqrt[4]{a+b x^4} (3 b c-a d)}{4 c d^2}-\frac{x \left(a+b x^4\right)^{5/4} (b c-a d)}{4 c d \left(c+d x^4\right)}",1,"(b*(3*b*c - a*d)*x*(a + b*x^4)^(1/4))/(4*c*d^2) - ((b*c - a*d)*x*(a + b*x^4)^(5/4))/(4*c*d*(c + d*x^4)) - (Sqrt[a]*b^(3/2)*(3*b*c - a*d)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*c*d^2*(a + b*x^4)^(3/4)) - (3*(b*c - a*d)*(2*b*c + a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*d^2) - (3*(b*c - a*d)*(2*b*c + a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*d^2)","A",11,10,21,0.4762,1,"{413, 528, 529, 237, 335, 275, 231, 407, 409, 1218}"
212,1,298,0,0.2397949,"\int \frac{\left(a+b x^4\right)^{5/4}}{\left(c+d x^4\right)^2} \, dx","Int[(a + b*x^4)^(5/4)/(c + d*x^4)^2,x]","\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 c d \left(a+b x^4\right)^{3/4}}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (3 a d+2 b c) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (3 a d+2 b c) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d}-\frac{x \sqrt[4]{a+b x^4} (b c-a d)}{4 c d \left(c+d x^4\right)}","\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 c d \left(a+b x^4\right)^{3/4}}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (3 a d+2 b c) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (3 a d+2 b c) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 d}-\frac{x \sqrt[4]{a+b x^4} (b c-a d)}{4 c d \left(c+d x^4\right)}",1,"-((b*c - a*d)*x*(a + b*x^4)^(1/4))/(4*c*d*(c + d*x^4)) + (Sqrt[a]*b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*c*d*(a + b*x^4)^(3/4)) + ((2*b*c + 3*a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*d) + ((2*b*c + 3*a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*d)","A",10,9,21,0.4286,1,"{413, 529, 237, 335, 275, 231, 407, 409, 1218}"
213,1,308,0,0.2034483,"\int \frac{\sqrt[4]{a+b x^4}}{\left(c+d x^4\right)^2} \, dx","Int[(a + b*x^4)^(1/4)/(c + d*x^4)^2,x]","-\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 c \left(a+b x^4\right)^{3/4} (b c-a d)}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (2 b c-3 a d) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (2 b c-3 a d) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)}+\frac{x \sqrt[4]{a+b x^4}}{4 c \left(c+d x^4\right)}","-\frac{\sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 c \left(a+b x^4\right)^{3/4} (b c-a d)}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (2 b c-3 a d) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)}+\frac{\sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (2 b c-3 a d) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)}+\frac{x \sqrt[4]{a+b x^4}}{4 c \left(c+d x^4\right)}",1,"(x*(a + b*x^4)^(1/4))/(4*c*(c + d*x^4)) - (Sqrt[a]*b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*c*(b*c - a*d)*(a + b*x^4)^(3/4)) + ((2*b*c - 3*a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)) + ((2*b*c - 3*a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d))","A",10,9,21,0.4286,1,"{412, 529, 237, 335, 275, 231, 407, 409, 1218}"
214,1,330,0,0.2495385,"\int \frac{1}{\left(a+b x^4\right)^{3/4} \left(c+d x^4\right)^2} \, dx","Int[1/((a + b*x^4)^(3/4)*(c + d*x^4)^2),x]","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} (4 b c-a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 \sqrt{a} c \left(a+b x^4\right)^{3/4} (b c-a d)^2}-\frac{3 d \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (2 b c-a d) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)^2}-\frac{3 d \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (2 b c-a d) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)^2}-\frac{d x \sqrt[4]{a+b x^4}}{4 c \left(c+d x^4\right) (b c-a d)}","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} (4 b c-a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 \sqrt{a} c \left(a+b x^4\right)^{3/4} (b c-a d)^2}-\frac{3 d \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (2 b c-a d) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)^2}-\frac{3 d \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (2 b c-a d) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)^2}-\frac{d x \sqrt[4]{a+b x^4}}{4 c \left(c+d x^4\right) (b c-a d)}",1,"-(d*x*(a + b*x^4)^(1/4))/(4*c*(b*c - a*d)*(c + d*x^4)) - (b^(3/2)*(4*b*c - a*d)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*Sqrt[a]*c*(b*c - a*d)^2*(a + b*x^4)^(3/4)) - (3*d*(2*b*c - a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)^2) - (3*d*(2*b*c - a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)^2)","A",10,9,21,0.4286,1,"{414, 529, 237, 335, 275, 231, 407, 409, 1218}"
215,1,390,0,0.4060089,"\int \frac{1}{\left(a+b x^4\right)^{7/4} \left(c+d x^4\right)^2} \, dx","Int[1/((a + b*x^4)^(7/4)*(c + d*x^4)^2),x]","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} \left(3 a^2 d^2-32 a b c d+8 b^2 c^2\right) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} c \left(a+b x^4\right)^{3/4} (b c-a d)^3}+\frac{d^2 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (10 b c-3 a d) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)^3}+\frac{d^2 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (10 b c-3 a d) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)^3}+\frac{b x (3 a d+4 b c)}{12 a c \left(a+b x^4\right)^{3/4} (b c-a d)^2}-\frac{d x}{4 c \left(a+b x^4\right)^{3/4} \left(c+d x^4\right) (b c-a d)}","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} \left(3 a^2 d^2-32 a b c d+8 b^2 c^2\right) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} c \left(a+b x^4\right)^{3/4} (b c-a d)^3}+\frac{d^2 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (10 b c-3 a d) \Pi \left(-\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)^3}+\frac{d^2 \sqrt{\frac{a}{a+b x^4}} \sqrt{a+b x^4} (10 b c-3 a d) \Pi \left(\frac{\sqrt{b c-a d}}{\sqrt{b} \sqrt{c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{b x^4+a}}\right)\right|-1\right)}{8 \sqrt[4]{b} c^2 (b c-a d)^3}+\frac{b x (3 a d+4 b c)}{12 a c \left(a+b x^4\right)^{3/4} (b c-a d)^2}-\frac{d x}{4 c \left(a+b x^4\right)^{3/4} \left(c+d x^4\right) (b c-a d)}",1,"(b*(4*b*c + 3*a*d)*x)/(12*a*c*(b*c - a*d)^2*(a + b*x^4)^(3/4)) - (d*x)/(4*c*(b*c - a*d)*(a + b*x^4)^(3/4)*(c + d*x^4)) - (b^(3/2)*(8*b^2*c^2 - 32*a*b*c*d + 3*a^2*d^2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*a^(3/2)*c*(b*c - a*d)^3*(a + b*x^4)^(3/4)) + (d^2*(10*b*c - 3*a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[-(Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c])), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)^3) + (d^2*(10*b*c - 3*a*d)*Sqrt[a/(a + b*x^4)]*Sqrt[a + b*x^4]*EllipticPi[Sqrt[b*c - a*d]/(Sqrt[b]*Sqrt[c]), ArcSin[(b^(1/4)*x)/(a + b*x^4)^(1/4)], -1])/(8*b^(1/4)*c^2*(b*c - a*d)^3)","A",11,10,21,0.4762,1,"{414, 527, 529, 237, 335, 275, 231, 407, 409, 1218}"
216,1,53,0,0.018443,"\int \frac{1}{\sqrt[4]{1+x^4} \left(2+x^4\right)} \, dx","Int[1/((1 + x^4)^(1/4)*(2 + x^4)),x]","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{2\ 2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{2\ 2^{3/4}}","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{2\ 2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{2\ 2^{3/4}}",1,"ArcTan[x/(2^(1/4)*(1 + x^4)^(1/4))]/(2*2^(3/4)) + ArcTanh[x/(2^(1/4)*(1 + x^4)^(1/4))]/(2*2^(3/4))","A",4,4,17,0.2353,1,"{377, 212, 206, 203}"
217,1,57,0,0.0223042,"\int \frac{1}{\left(a-(a-b) x^4\right) \sqrt[4]{a+b x^4}} \, dx","Int[1/((a - (a - b)*x^4)*(a + b*x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}\right)}{2 a^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}\right)}{2 a^{5/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}\right)}{2 a^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}\right)}{2 a^{5/4}}",1,"ArcTan[(a^(1/4)*x)/(a + b*x^4)^(1/4)]/(2*a^(5/4)) + ArcTanh[(a^(1/4)*x)/(a + b*x^4)^(1/4)]/(2*a^(5/4))","A",4,4,26,0.1538,1,"{377, 212, 206, 203}"
218,1,79,0,0.0472042,"\int \left(a+b x^4\right)^p \left(c+d x^4\right)^q \, dx","Int[(a + b*x^4)^p*(c + d*x^4)^q,x]","x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} F_1\left(\frac{1}{4};-p,-q;\frac{5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)","x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} F_1\left(\frac{1}{4};-p,-q;\frac{5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)",1,"(x*(a + b*x^4)^p*(c + d*x^4)^q*AppellF1[1/4, -p, -q, 5/4, -((b*x^4)/a), -((d*x^4)/c)])/((1 + (b*x^4)/a)^p*(1 + (d*x^4)/c)^q)","A",3,2,19,0.1053,1,"{430, 429}"
219,1,176,0,0.1330635,"\int \left(a+b x^4\right)^2 \left(c+d x^4\right)^q \, dx","Int[(a + b*x^4)^2*(c + d*x^4)^q,x]","\frac{x \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} \left(a^2 d^2 \left(16 q^2+56 q+45\right)-2 a b c d (4 q+9)+5 b^2 c^2\right) \, _2F_1\left(\frac{1}{4},-q;\frac{5}{4};-\frac{d x^4}{c}\right)}{d^2 (4 q+5) (4 q+9)}-\frac{b x \left(c+d x^4\right)^{q+1} (5 b c-a d (4 q+13))}{d^2 (4 q+5) (4 q+9)}+\frac{b x \left(a+b x^4\right) \left(c+d x^4\right)^{q+1}}{d (4 q+9)}","\frac{x \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} \left(a^2 d^2 \left(16 q^2+56 q+45\right)-2 a b c d (4 q+9)+5 b^2 c^2\right) \, _2F_1\left(\frac{1}{4},-q;\frac{5}{4};-\frac{d x^4}{c}\right)}{d^2 (4 q+5) (4 q+9)}-\frac{b x \left(c+d x^4\right)^{q+1} (5 b c-a d (4 q+13))}{d^2 (4 q+5) (4 q+9)}+\frac{b x \left(a+b x^4\right) \left(c+d x^4\right)^{q+1}}{d (4 q+9)}",1,"-((b*(5*b*c - a*d*(13 + 4*q))*x*(c + d*x^4)^(1 + q))/(d^2*(5 + 4*q)*(9 + 4*q))) + (b*x*(a + b*x^4)*(c + d*x^4)^(1 + q))/(d*(9 + 4*q)) + ((5*b^2*c^2 - 2*a*b*c*d*(9 + 4*q) + a^2*d^2*(45 + 56*q + 16*q^2))*x*(c + d*x^4)^q*Hypergeometric2F1[1/4, -q, 5/4, -((d*x^4)/c)])/(d^2*(5 + 4*q)*(9 + 4*q)*(1 + (d*x^4)/c)^q)","A",4,4,19,0.2105,1,"{416, 388, 246, 245}"
220,1,85,0,0.0407276,"\int \left(a+b x^4\right) \left(c+d x^4\right)^q \, dx","Int[(a + b*x^4)*(c + d*x^4)^q,x]","x \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} \left(a-\frac{b c}{4 d q+5 d}\right) \, _2F_1\left(\frac{1}{4},-q;\frac{5}{4};-\frac{d x^4}{c}\right)+\frac{b x \left(c+d x^4\right)^{q+1}}{d (4 q+5)}","\frac{b x \left(c+d x^4\right)^{q+1}}{d (4 q+5)}-\frac{x \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} (b c-a d (4 q+5)) \, _2F_1\left(\frac{1}{4},-q;\frac{5}{4};-\frac{d x^4}{c}\right)}{d (4 q+5)}",1,"(b*x*(c + d*x^4)^(1 + q))/(d*(5 + 4*q)) + ((a - (b*c)/(5*d + 4*d*q))*x*(c + d*x^4)^q*Hypergeometric2F1[1/4, -q, 5/4, -((d*x^4)/c)])/(1 + (d*x^4)/c)^q","A",3,3,17,0.1765,1,"{388, 246, 245}"
221,1,57,0,0.0286241,"\int \frac{\left(c+d x^4\right)^q}{a+b x^4} \, dx","Int[(c + d*x^4)^q/(a + b*x^4),x]","\frac{x \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} F_1\left(\frac{1}{4};1,-q;\frac{5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a}","\frac{x \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} F_1\left(\frac{1}{4};1,-q;\frac{5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a}",1,"(x*(c + d*x^4)^q*AppellF1[1/4, 1, -q, 5/4, -((b*x^4)/a), -((d*x^4)/c)])/(a*(1 + (d*x^4)/c)^q)","A",2,2,19,0.1053,1,"{430, 429}"
222,1,57,0,0.0276523,"\int \frac{\left(c+d x^4\right)^q}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x^4)^q/(a + b*x^4)^2,x]","\frac{x \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} F_1\left(\frac{1}{4};2,-q;\frac{5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^2}","\frac{x \left(c+d x^4\right)^q \left(\frac{d x^4}{c}+1\right)^{-q} F_1\left(\frac{1}{4};2,-q;\frac{5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^2}",1,"(x*(c + d*x^4)^q*AppellF1[1/4, 2, -q, 5/4, -((b*x^4)/a), -((d*x^4)/c)])/(a^2*(1 + (d*x^4)/c)^q)","A",2,2,19,0.1053,1,"{430, 429}"
223,1,545,0,1.0850701,"\int \frac{1}{\sqrt[5]{a+b x^5} \left(c+d x^5\right)} \, dx","Int[1/((a + b*x^5)^(1/5)*(c + d*x^5)),x]","-\frac{\log \left(\sqrt[5]{c}-\frac{x \sqrt[5]{b c-a d}}{\sqrt[5]{a+b x^5}}\right)}{5 c^{4/5} \sqrt[5]{b c-a d}}+\frac{\left(1-\sqrt{5}\right) \log \left(\frac{2 c^{2/5} \left(a+b x^5\right)^{2/5}+2 x^2 (b c-a d)^{2/5}-\sqrt{5} \sqrt[5]{c} x \sqrt[5]{a+b x^5} \sqrt[5]{b c-a d}+\sqrt[5]{c} x \sqrt[5]{a+b x^5} \sqrt[5]{b c-a d}}{\left(a+b x^5\right)^{2/5}}\right)}{20 c^{4/5} \sqrt[5]{b c-a d}}+\frac{\left(1+\sqrt{5}\right) \log \left(\frac{2 c^{2/5} \left(a+b x^5\right)^{2/5}+2 x^2 (b c-a d)^{2/5}+\sqrt{5} \sqrt[5]{c} x \sqrt[5]{a+b x^5} \sqrt[5]{b c-a d}+\sqrt[5]{c} x \sqrt[5]{a+b x^5} \sqrt[5]{b c-a d}}{\left(a+b x^5\right)^{2/5}}\right)}{20 c^{4/5} \sqrt[5]{b c-a d}}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}-\frac{2 \sqrt{\frac{2}{5+\sqrt{5}}} x \sqrt[5]{b c-a d}}{\sqrt[5]{c} \sqrt[5]{a+b x^5}}\right)}{5 c^{4/5} \sqrt[5]{b c-a d}}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x \sqrt[5]{b c-a d}}{\sqrt[5]{c} \sqrt[5]{a+b x^5}}+\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}\right)}{5 c^{4/5} \sqrt[5]{b c-a d}}","-\frac{\log \left(\sqrt[5]{c}-\frac{x \sqrt[5]{b c-a d}}{\sqrt[5]{a+b x^5}}\right)}{5 c^{4/5} \sqrt[5]{b c-a d}}+\frac{\left(1-\sqrt{5}\right) \log \left(\frac{2 c^{2/5} \left(a+b x^5\right)^{2/5}+2 x^2 (b c-a d)^{2/5}-\sqrt{5} \sqrt[5]{c} x \sqrt[5]{a+b x^5} \sqrt[5]{b c-a d}+\sqrt[5]{c} x \sqrt[5]{a+b x^5} \sqrt[5]{b c-a d}}{\left(a+b x^5\right)^{2/5}}\right)}{20 c^{4/5} \sqrt[5]{b c-a d}}+\frac{\left(1+\sqrt{5}\right) \log \left(\frac{2 c^{2/5} \left(a+b x^5\right)^{2/5}+2 x^2 (b c-a d)^{2/5}+\sqrt{5} \sqrt[5]{c} x \sqrt[5]{a+b x^5} \sqrt[5]{b c-a d}+\sqrt[5]{c} x \sqrt[5]{a+b x^5} \sqrt[5]{b c-a d}}{\left(a+b x^5\right)^{2/5}}\right)}{20 c^{4/5} \sqrt[5]{b c-a d}}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}-\frac{2 \sqrt{\frac{2}{5+\sqrt{5}}} x \sqrt[5]{b c-a d}}{\sqrt[5]{c} \sqrt[5]{a+b x^5}}\right)}{5 c^{4/5} \sqrt[5]{b c-a d}}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x \sqrt[5]{b c-a d}}{\sqrt[5]{c} \sqrt[5]{a+b x^5}}+\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}\right)}{5 c^{4/5} \sqrt[5]{b c-a d}}",1,"-(Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] - (2*Sqrt[2/(5 + Sqrt[5])]*(b*c - a*d)^(1/5)*x)/(c^(1/5)*(a + b*x^5)^(1/5))])/(5*c^(4/5)*(b*c - a*d)^(1/5)) + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] + (Sqrt[(2*(5 + Sqrt[5]))/5]*(b*c - a*d)^(1/5)*x)/(c^(1/5)*(a + b*x^5)^(1/5))])/(5*c^(4/5)*(b*c - a*d)^(1/5)) - Log[c^(1/5) - ((b*c - a*d)^(1/5)*x)/(a + b*x^5)^(1/5)]/(5*c^(4/5)*(b*c - a*d)^(1/5)) + ((1 - Sqrt[5])*Log[(2*(b*c - a*d)^(2/5)*x^2 + c^(1/5)*(b*c - a*d)^(1/5)*x*(a + b*x^5)^(1/5) - Sqrt[5]*c^(1/5)*(b*c - a*d)^(1/5)*x*(a + b*x^5)^(1/5) + 2*c^(2/5)*(a + b*x^5)^(2/5))/(a + b*x^5)^(2/5)])/(20*c^(4/5)*(b*c - a*d)^(1/5)) + ((1 + Sqrt[5])*Log[(2*(b*c - a*d)^(2/5)*x^2 + c^(1/5)*(b*c - a*d)^(1/5)*x*(a + b*x^5)^(1/5) + Sqrt[5]*c^(1/5)*(b*c - a*d)^(1/5)*x*(a + b*x^5)^(1/5) + 2*c^(2/5)*(a + b*x^5)^(2/5))/(a + b*x^5)^(2/5)])/(20*c^(4/5)*(b*c - a*d)^(1/5))","A",7,7,21,0.3333,1,"{377, 202, 634, 618, 204, 628, 31}"
224,1,143,0,0.1233153,"\int \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^3 \, dx","Int[Sqrt[a + b/x]*(c + d/x)^3,x]","-\frac{d \sqrt{a+\frac{b}{x}} \left(2 \left(-2 a^2 d^2+15 a b c d+57 b^2 c^2\right)+\frac{b d (2 a d+33 b c)}{x}\right)}{15 b^2}+\frac{c^2 (6 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}+x \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^3-\frac{7}{5} d \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2","-\frac{d \sqrt{a+\frac{b}{x}} \left(2 \left(-2 a^2 d^2+15 a b c d+57 b^2 c^2\right)+\frac{b d (2 a d+33 b c)}{x}\right)}{15 b^2}+\frac{c^2 (6 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}+x \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^3-\frac{7}{5} d \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2",1,"(-7*d*Sqrt[a + b/x]*(c + d/x)^2)/5 - (d*Sqrt[a + b/x]*(2*(57*b^2*c^2 + 15*a*b*c*d - 2*a^2*d^2) + (b*d*(33*b*c + 2*a*d))/x))/(15*b^2) + Sqrt[a + b/x]*(c + d/x)^3*x + (c^2*(b*c + 6*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/Sqrt[a]","A",6,6,21,0.2857,1,"{375, 97, 153, 147, 63, 208}"
225,1,99,0,0.0666848,"\int \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2 \, dx","Int[Sqrt[a + b/x]*(c + d/x)^2,x]","\frac{c^2 x \left(a+\frac{b}{x}\right)^{3/2}}{a}-\frac{c \sqrt{a+\frac{b}{x}} (4 a d+b c)}{a}+\frac{c (4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{2 d^2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b}","\frac{c^2 x \left(a+\frac{b}{x}\right)^{3/2}}{a}-\frac{c \sqrt{a+\frac{b}{x}} (4 a d+b c)}{a}+\frac{c (4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{2 d^2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b}",1,"-((c*(b*c + 4*a*d)*Sqrt[a + b/x])/a) - (2*d^2*(a + b/x)^(3/2))/(3*b) + (c^2*(a + b/x)^(3/2)*x)/a + (c*(b*c + 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/Sqrt[a]","A",6,6,21,0.2857,1,"{375, 89, 80, 50, 63, 208}"
226,1,74,0,0.0483524,"\int \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right) \, dx","Int[Sqrt[a + b/x]*(c + d/x),x]","-\frac{\sqrt{a+\frac{b}{x}} (2 a d+b c)}{a}+\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}+\frac{c x \left(a+\frac{b}{x}\right)^{3/2}}{a}","-\frac{\sqrt{a+\frac{b}{x}} (2 a d+b c)}{a}+\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}+\frac{c x \left(a+\frac{b}{x}\right)^{3/2}}{a}",1,"-(((b*c + 2*a*d)*Sqrt[a + b/x])/a) + (c*(a + b/x)^(3/2)*x)/a + ((b*c + 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/Sqrt[a]","A",5,5,19,0.2632,1,"{375, 78, 50, 63, 208}"
227,1,39,0,0.018864,"\int \sqrt{a+\frac{b}{x}} \, dx","Int[Sqrt[a + b/x],x]","x \sqrt{a+\frac{b}{x}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}","x \sqrt{a+\frac{b}{x}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"Sqrt[a + b/x]*x + (b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/Sqrt[a]","A",4,4,11,0.3636,1,"{242, 47, 63, 208}"
228,1,104,0,0.1106252,"\int \frac{\sqrt{a+\frac{b}{x}}}{c+\frac{d}{x}} \, dx","Int[Sqrt[a + b/x]/(c + d/x),x]","\frac{2 \sqrt{d} \sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2}+\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a} c^2}+\frac{x \sqrt{a+\frac{b}{x}}}{c}","\frac{2 \sqrt{d} \sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2}+\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a} c^2}+\frac{x \sqrt{a+\frac{b}{x}}}{c}",1,"(Sqrt[a + b/x]*x)/c + (2*Sqrt[d]*Sqrt[b*c - a*d]*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/c^2 + ((b*c - 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(Sqrt[a]*c^2)","A",7,6,21,0.2857,1,"{375, 99, 156, 63, 208, 205}"
229,1,147,0,0.2086268,"\int \frac{\sqrt{a+\frac{b}{x}}}{\left(c+\frac{d}{x}\right)^2} \, dx","Int[Sqrt[a + b/x]/(c + d/x)^2,x]","\frac{2 d \sqrt{a+\frac{b}{x}}}{c^2 \left(c+\frac{d}{x}\right)}+\frac{\sqrt{d} (3 b c-4 a d) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 \sqrt{b c-a d}}+\frac{(b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a} c^3}+\frac{x \sqrt{a+\frac{b}{x}}}{c \left(c+\frac{d}{x}\right)}","\frac{2 d \sqrt{a+\frac{b}{x}}}{c^2 \left(c+\frac{d}{x}\right)}+\frac{\sqrt{d} (3 b c-4 a d) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 \sqrt{b c-a d}}+\frac{(b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a} c^3}+\frac{x \sqrt{a+\frac{b}{x}}}{c \left(c+\frac{d}{x}\right)}",1,"(2*d*Sqrt[a + b/x])/(c^2*(c + d/x)) + (Sqrt[a + b/x]*x)/(c*(c + d/x)) + (Sqrt[d]*(3*b*c - 4*a*d)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^3*Sqrt[b*c - a*d]) + ((b*c - 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(Sqrt[a]*c^3)","A",8,7,21,0.3333,1,"{375, 99, 151, 156, 63, 208, 205}"
230,1,213,0,0.3395863,"\int \frac{\sqrt{a+\frac{b}{x}}}{\left(c+\frac{d}{x}\right)^3} \, dx","Int[Sqrt[a + b/x]/(c + d/x)^3,x]","\frac{\sqrt{d} \left(24 a^2 d^2-40 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 (b c-a d)^{3/2}}+\frac{d \sqrt{a+\frac{b}{x}} (11 b c-12 a d)}{4 c^3 \left(c+\frac{d}{x}\right) (b c-a d)}+\frac{3 d \sqrt{a+\frac{b}{x}}}{2 c^2 \left(c+\frac{d}{x}\right)^2}+\frac{(b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a} c^4}+\frac{x \sqrt{a+\frac{b}{x}}}{c \left(c+\frac{d}{x}\right)^2}","\frac{\sqrt{d} \left(24 a^2 d^2-40 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 (b c-a d)^{3/2}}+\frac{d \sqrt{a+\frac{b}{x}} (11 b c-12 a d)}{4 c^3 \left(c+\frac{d}{x}\right) (b c-a d)}+\frac{3 d \sqrt{a+\frac{b}{x}}}{2 c^2 \left(c+\frac{d}{x}\right)^2}+\frac{(b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a} c^4}+\frac{x \sqrt{a+\frac{b}{x}}}{c \left(c+\frac{d}{x}\right)^2}",1,"(3*d*Sqrt[a + b/x])/(2*c^2*(c + d/x)^2) + (d*(11*b*c - 12*a*d)*Sqrt[a + b/x])/(4*c^3*(b*c - a*d)*(c + d/x)) + (Sqrt[a + b/x]*x)/(c*(c + d/x)^2) + (Sqrt[d]*(15*b^2*c^2 - 40*a*b*c*d + 24*a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(4*c^4*(b*c - a*d)^(3/2)) + ((b*c - 6*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(Sqrt[a]*c^4)","A",9,7,21,0.3333,1,"{375, 99, 151, 156, 63, 208, 205}"
231,1,164,0,0.1418657,"\int \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^3 \, dx","Int[(a + b/x)^(3/2)*(c + d/x)^3,x]","-\frac{d \left(a+\frac{b}{x}\right)^{3/2} \left(\frac{3 b d (2 a d+19 b c)}{x}+2 (13 b c-a d) (2 a d+5 b c)\right)}{35 b^2}-3 c^2 \sqrt{a+\frac{b}{x}} (2 a d+b c)+3 \sqrt{a} c^2 (2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+x \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^3-\frac{9}{7} d \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^2","-\frac{d \left(a+\frac{b}{x}\right)^{3/2} \left(\frac{3 b d (2 a d+19 b c)}{x}+2 (13 b c-a d) (2 a d+5 b c)\right)}{35 b^2}-3 c^2 \sqrt{a+\frac{b}{x}} (2 a d+b c)+3 \sqrt{a} c^2 (2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+x \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^3-\frac{9}{7} d \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^2",1,"-3*c^2*(b*c + 2*a*d)*Sqrt[a + b/x] - (9*d*(a + b/x)^(3/2)*(c + d/x)^2)/7 - (d*(a + b/x)^(3/2)*(2*(13*b*c - a*d)*(5*b*c + 2*a*d) + (3*b*d*(19*b*c + 2*a*d))/x))/(35*b^2) + (a + b/x)^(3/2)*(c + d/x)^3*x + 3*Sqrt[a]*c^2*(b*c + 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",7,7,21,0.3333,1,"{375, 97, 153, 147, 50, 63, 208}"
232,1,126,0,0.0795285,"\int \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^2 \, dx","Int[(a + b/x)^(3/2)*(c + d/x)^2,x]","\frac{c^2 x \left(a+\frac{b}{x}\right)^{5/2}}{a}-\frac{c \left(a+\frac{b}{x}\right)^{3/2} (4 a d+3 b c)}{3 a}-c \sqrt{a+\frac{b}{x}} (4 a d+3 b c)+\sqrt{a} c (4 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{2 d^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b}","\frac{c^2 x \left(a+\frac{b}{x}\right)^{5/2}}{a}-\frac{c \left(a+\frac{b}{x}\right)^{3/2} (4 a d+3 b c)}{3 a}-c \sqrt{a+\frac{b}{x}} (4 a d+3 b c)+\sqrt{a} c (4 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{2 d^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b}",1,"-(c*(3*b*c + 4*a*d)*Sqrt[a + b/x]) - (c*(3*b*c + 4*a*d)*(a + b/x)^(3/2))/(3*a) - (2*d^2*(a + b/x)^(5/2))/(5*b) + (c^2*(a + b/x)^(5/2)*x)/a + Sqrt[a]*c*(3*b*c + 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",7,6,21,0.2857,1,"{375, 89, 80, 50, 63, 208}"
233,1,100,0,0.0627703,"\int \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right) \, dx","Int[(a + b/x)^(3/2)*(c + d/x),x]","-\frac{\left(a+\frac{b}{x}\right)^{3/2} (2 a d+3 b c)}{3 a}-\sqrt{a+\frac{b}{x}} (2 a d+3 b c)+\sqrt{a} (2 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+\frac{c x \left(a+\frac{b}{x}\right)^{5/2}}{a}","-\frac{\left(a+\frac{b}{x}\right)^{3/2} (2 a d+3 b c)}{3 a}-\sqrt{a+\frac{b}{x}} (2 a d+3 b c)+\sqrt{a} (2 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+\frac{c x \left(a+\frac{b}{x}\right)^{5/2}}{a}",1,"-((3*b*c + 2*a*d)*Sqrt[a + b/x]) - ((3*b*c + 2*a*d)*(a + b/x)^(3/2))/(3*a) + (c*(a + b/x)^(5/2)*x)/a + Sqrt[a]*(3*b*c + 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",6,5,19,0.2632,1,"{375, 78, 50, 63, 208}"
234,1,54,0,0.0253246,"\int \left(a+\frac{b}{x}\right)^{3/2} \, dx","Int[(a + b/x)^(3/2),x]","x \left(a+\frac{b}{x}\right)^{3/2}-3 b \sqrt{a+\frac{b}{x}}+3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)","x \left(a+\frac{b}{x}\right)^{3/2}-3 b \sqrt{a+\frac{b}{x}}+3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)",1,"-3*b*Sqrt[a + b/x] + (a + b/x)^(3/2)*x + 3*Sqrt[a]*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",5,5,11,0.4545,1,"{242, 47, 50, 63, 208}"
235,1,106,0,0.1283299,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{c+\frac{d}{x}} \, dx","Int[(a + b/x)^(3/2)/(c + d/x),x]","-\frac{2 (b c-a d)^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 \sqrt{d}}+\frac{\sqrt{a} (3 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^2}+\frac{a x \sqrt{a+\frac{b}{x}}}{c}","-\frac{2 (b c-a d)^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 \sqrt{d}}+\frac{\sqrt{a} (3 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^2}+\frac{a x \sqrt{a+\frac{b}{x}}}{c}",1,"(a*Sqrt[a + b/x]*x)/c - (2*(b*c - a*d)^(3/2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^2*Sqrt[d]) + (Sqrt[a]*(3*b*c - 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/c^2","A",7,6,21,0.2857,1,"{375, 98, 156, 63, 208, 205}"
236,1,156,0,0.2218307,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{\left(c+\frac{d}{x}\right)^2} \, dx","Int[(a + b/x)^(3/2)/(c + d/x)^2,x]","-\frac{\sqrt{a+\frac{b}{x}} (b c-2 a d)}{c^2 \left(c+\frac{d}{x}\right)}-\frac{(b c-4 a d) \sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 \sqrt{d}}+\frac{\sqrt{a} (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^3}+\frac{a x \sqrt{a+\frac{b}{x}}}{c \left(c+\frac{d}{x}\right)}","-\frac{\sqrt{a+\frac{b}{x}} (b c-2 a d)}{c^2 \left(c+\frac{d}{x}\right)}-\frac{(b c-4 a d) \sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 \sqrt{d}}+\frac{\sqrt{a} (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^3}+\frac{a x \sqrt{a+\frac{b}{x}}}{c \left(c+\frac{d}{x}\right)}",1,"-(((b*c - 2*a*d)*Sqrt[a + b/x])/(c^2*(c + d/x))) + (a*Sqrt[a + b/x]*x)/(c*(c + d/x)) - ((b*c - 4*a*d)*Sqrt[b*c - a*d]*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^3*Sqrt[d]) + (Sqrt[a]*(3*b*c - 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/c^3","A",8,7,21,0.3333,1,"{375, 98, 151, 156, 63, 208, 205}"
237,1,209,0,0.3449805,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{\left(c+\frac{d}{x}\right)^3} \, dx","Int[(a + b/x)^(3/2)/(c + d/x)^3,x]","-\frac{3 \left(8 a^2 d^2-8 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 \sqrt{d} \sqrt{b c-a d}}-\frac{3 \sqrt{a+\frac{b}{x}} (b c-4 a d)}{4 c^3 \left(c+\frac{d}{x}\right)}-\frac{\sqrt{a+\frac{b}{x}} (b c-3 a d)}{2 c^2 \left(c+\frac{d}{x}\right)^2}+\frac{3 \sqrt{a} (b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^4}+\frac{a x \sqrt{a+\frac{b}{x}}}{c \left(c+\frac{d}{x}\right)^2}","-\frac{3 \left(8 a^2 d^2-8 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 \sqrt{d} \sqrt{b c-a d}}-\frac{3 \sqrt{a+\frac{b}{x}} (b c-4 a d)}{4 c^3 \left(c+\frac{d}{x}\right)}-\frac{\sqrt{a+\frac{b}{x}} (b c-3 a d)}{2 c^2 \left(c+\frac{d}{x}\right)^2}+\frac{3 \sqrt{a} (b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^4}+\frac{a x \sqrt{a+\frac{b}{x}}}{c \left(c+\frac{d}{x}\right)^2}",1,"-((b*c - 3*a*d)*Sqrt[a + b/x])/(2*c^2*(c + d/x)^2) - (3*(b*c - 4*a*d)*Sqrt[a + b/x])/(4*c^3*(c + d/x)) + (a*Sqrt[a + b/x]*x)/(c*(c + d/x)^2) - (3*(b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(4*c^4*Sqrt[d]*Sqrt[b*c - a*d]) + (3*Sqrt[a]*(b*c - 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/c^4","A",9,7,21,0.3333,1,"{375, 98, 151, 156, 63, 208, 205}"
238,1,198,0,0.1582982,"\int \left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)^3 \, dx","Int[(a + b/x)^(5/2)*(c + d/x)^3,x]","-\frac{d \left(a+\frac{b}{x}\right)^{5/2} \left(2 \left(-10 a^2 d^2+135 a b c d+469 b^2 c^2\right)+\frac{5 b d (10 a d+89 b c)}{x}\right)}{315 b^2}+a^{3/2} c^2 (6 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{1}{3} c^2 \left(a+\frac{b}{x}\right)^{3/2} (6 a d+5 b c)-a c^2 \sqrt{a+\frac{b}{x}} (6 a d+5 b c)+x \left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)^3-\frac{11}{9} d \left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)^2","-\frac{d \left(a+\frac{b}{x}\right)^{5/2} \left(2 \left(-10 a^2 d^2+135 a b c d+469 b^2 c^2\right)+\frac{5 b d (10 a d+89 b c)}{x}\right)}{315 b^2}+a^{3/2} c^2 (6 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{1}{3} c^2 \left(a+\frac{b}{x}\right)^{3/2} (6 a d+5 b c)-a c^2 \sqrt{a+\frac{b}{x}} (6 a d+5 b c)+x \left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)^3-\frac{11}{9} d \left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)^2",1,"-(a*c^2*(5*b*c + 6*a*d)*Sqrt[a + b/x]) - (c^2*(5*b*c + 6*a*d)*(a + b/x)^(3/2))/3 - (11*d*(a + b/x)^(5/2)*(c + d/x)^2)/9 - (d*(a + b/x)^(5/2)*(2*(469*b^2*c^2 + 135*a*b*c*d - 10*a^2*d^2) + (5*b*d*(89*b*c + 10*a*d))/x))/(315*b^2) + (a + b/x)^(5/2)*(c + d/x)^3*x + a^(3/2)*c^2*(5*b*c + 6*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",8,7,21,0.3333,1,"{375, 97, 153, 147, 50, 63, 208}"
239,1,152,0,0.1020391,"\int \left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)^2 \, dx","Int[(a + b/x)^(5/2)*(c + d/x)^2,x]","a^{3/2} c (4 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+\frac{c^2 x \left(a+\frac{b}{x}\right)^{7/2}}{a}-\frac{c \left(a+\frac{b}{x}\right)^{5/2} (4 a d+5 b c)}{5 a}-\frac{1}{3} c \left(a+\frac{b}{x}\right)^{3/2} (4 a d+5 b c)-a c \sqrt{a+\frac{b}{x}} (4 a d+5 b c)-\frac{2 d^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b}","a^{3/2} c (4 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+\frac{c^2 x \left(a+\frac{b}{x}\right)^{7/2}}{a}-\frac{c \left(a+\frac{b}{x}\right)^{5/2} (4 a d+5 b c)}{5 a}-\frac{1}{3} c \left(a+\frac{b}{x}\right)^{3/2} (4 a d+5 b c)-a c \sqrt{a+\frac{b}{x}} (4 a d+5 b c)-\frac{2 d^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b}",1,"-(a*c*(5*b*c + 4*a*d)*Sqrt[a + b/x]) - (c*(5*b*c + 4*a*d)*(a + b/x)^(3/2))/3 - (c*(5*b*c + 4*a*d)*(a + b/x)^(5/2))/(5*a) - (2*d^2*(a + b/x)^(7/2))/(7*b) + (c^2*(a + b/x)^(7/2)*x)/a + a^(3/2)*c*(5*b*c + 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",8,6,21,0.2857,1,"{375, 89, 80, 50, 63, 208}"
240,1,125,0,0.0766491,"\int \left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right) \, dx","Int[(a + b/x)^(5/2)*(c + d/x),x]","a^{3/2} (2 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{\left(a+\frac{b}{x}\right)^{5/2} (2 a d+5 b c)}{5 a}-\frac{1}{3} \left(a+\frac{b}{x}\right)^{3/2} (2 a d+5 b c)-a \sqrt{a+\frac{b}{x}} (2 a d+5 b c)+\frac{c x \left(a+\frac{b}{x}\right)^{7/2}}{a}","a^{3/2} (2 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{\left(a+\frac{b}{x}\right)^{5/2} (2 a d+5 b c)}{5 a}-\frac{1}{3} \left(a+\frac{b}{x}\right)^{3/2} (2 a d+5 b c)-a \sqrt{a+\frac{b}{x}} (2 a d+5 b c)+\frac{c x \left(a+\frac{b}{x}\right)^{7/2}}{a}",1,"-(a*(5*b*c + 2*a*d)*Sqrt[a + b/x]) - ((5*b*c + 2*a*d)*(a + b/x)^(3/2))/3 - ((5*b*c + 2*a*d)*(a + b/x)^(5/2))/(5*a) + (c*(a + b/x)^(7/2)*x)/a + a^(3/2)*(5*b*c + 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",7,5,19,0.2632,1,"{375, 78, 50, 63, 208}"
241,1,71,0,0.0343127,"\int \left(a+\frac{b}{x}\right)^{5/2} \, dx","Int[(a + b/x)^(5/2),x]","5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+x \left(a+\frac{b}{x}\right)^{5/2}-\frac{5}{3} b \left(a+\frac{b}{x}\right)^{3/2}-5 a b \sqrt{a+\frac{b}{x}}","5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+x \left(a+\frac{b}{x}\right)^{5/2}-\frac{5}{3} b \left(a+\frac{b}{x}\right)^{3/2}-5 a b \sqrt{a+\frac{b}{x}}",1,"-5*a*b*Sqrt[a + b/x] - (5*b*(a + b/x)^(3/2))/3 + (a + b/x)^(5/2)*x + 5*a^(3/2)*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",6,5,11,0.4545,1,"{242, 47, 50, 63, 208}"
242,1,134,0,0.2213433,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{c+\frac{d}{x}} \, dx","Int[(a + b/x)^(5/2)/(c + d/x),x]","\frac{a^{3/2} (5 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^2}+\frac{2 (b c-a d)^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 d^{3/2}}-\frac{b \sqrt{a+\frac{b}{x}} (a d+2 b c)}{c d}+\frac{a x \left(a+\frac{b}{x}\right)^{3/2}}{c}","\frac{a^{3/2} (5 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^2}+\frac{2 (b c-a d)^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 d^{3/2}}-\frac{b \sqrt{a+\frac{b}{x}} (a d+2 b c)}{c d}+\frac{a x \left(a+\frac{b}{x}\right)^{3/2}}{c}",1,"-((b*(2*b*c + a*d)*Sqrt[a + b/x])/(c*d)) + (a*(a + b/x)^(3/2)*x)/c + (2*(b*c - a*d)^(5/2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^2*d^(3/2)) + (a^(3/2)*(5*b*c - 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/c^2","A",8,7,21,0.3333,1,"{375, 98, 154, 156, 63, 208, 205}"
243,1,166,0,0.2338583,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{\left(c+\frac{d}{x}\right)^2} \, dx","Int[(a + b/x)^(5/2)/(c + d/x)^2,x]","\frac{a^{3/2} (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^3}-\frac{(b c-a d)^{3/2} (4 a d+b c) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 d^{3/2}}+\frac{\sqrt{a+\frac{b}{x}} (b c-2 a d) (b c-a d)}{c^2 d \left(c+\frac{d}{x}\right)}+\frac{a x \left(a+\frac{b}{x}\right)^{3/2}}{c \left(c+\frac{d}{x}\right)}","\frac{a^{3/2} (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^3}-\frac{(b c-a d)^{3/2} (4 a d+b c) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 d^{3/2}}+\frac{\sqrt{a+\frac{b}{x}} (b c-2 a d) (b c-a d)}{c^2 d \left(c+\frac{d}{x}\right)}+\frac{a x \left(a+\frac{b}{x}\right)^{3/2}}{c \left(c+\frac{d}{x}\right)}",1,"((b*c - 2*a*d)*(b*c - a*d)*Sqrt[a + b/x])/(c^2*d*(c + d/x)) + (a*(a + b/x)^(3/2)*x)/(c*(c + d/x)) - ((b*c - a*d)^(3/2)*(b*c + 4*a*d)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^3*d^(3/2)) + (a^(3/2)*(5*b*c - 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/c^3","A",8,7,21,0.3333,1,"{375, 98, 149, 156, 63, 208, 205}"
244,1,237,0,0.3726792,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{\left(c+\frac{d}{x}\right)^3} \, dx","Int[(a + b/x)^(5/2)/(c + d/x)^3,x]","-\frac{\sqrt{a+\frac{b}{x}} \left(-12 a^2 d^2+7 a b c d+b^2 c^2\right)}{4 c^3 d \left(c+\frac{d}{x}\right)}-\frac{\sqrt{b c-a d} \left(-24 a^2 d^2+8 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 d^{3/2}}+\frac{a^{3/2} (5 b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^4}+\frac{\sqrt{a+\frac{b}{x}} (b c-3 a d) (b c-a d)}{2 c^2 d \left(c+\frac{d}{x}\right)^2}+\frac{a x \left(a+\frac{b}{x}\right)^{3/2}}{c \left(c+\frac{d}{x}\right)^2}","-\frac{\sqrt{a+\frac{b}{x}} \left(-12 a^2 d^2+7 a b c d+b^2 c^2\right)}{4 c^3 d \left(c+\frac{d}{x}\right)}-\frac{\sqrt{b c-a d} \left(-24 a^2 d^2+8 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 d^{3/2}}+\frac{a^{3/2} (5 b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{c^4}+\frac{\sqrt{a+\frac{b}{x}} (b c-3 a d) (b c-a d)}{2 c^2 d \left(c+\frac{d}{x}\right)^2}+\frac{a x \left(a+\frac{b}{x}\right)^{3/2}}{c \left(c+\frac{d}{x}\right)^2}",1,"((b*c - 3*a*d)*(b*c - a*d)*Sqrt[a + b/x])/(2*c^2*d*(c + d/x)^2) - ((b^2*c^2 + 7*a*b*c*d - 12*a^2*d^2)*Sqrt[a + b/x])/(4*c^3*d*(c + d/x)) + (a*(a + b/x)^(3/2)*x)/(c*(c + d/x)^2) - (Sqrt[b*c - a*d]*(b^2*c^2 + 8*a*b*c*d - 24*a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(4*c^4*d^(3/2)) + (a^(3/2)*(5*b*c - 6*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/c^4","A",9,8,21,0.3810,1,"{375, 98, 149, 151, 156, 63, 208, 205}"
245,1,126,0,0.0899013,"\int \frac{\left(c+\frac{d}{x}\right)^3}{\sqrt{a+\frac{b}{x}}} \, dx","Int[(c + d/x)^3/Sqrt[a + b/x],x]","-\frac{d \sqrt{a+\frac{b}{x}} \left(2 \left(-2 a^2 d^2+9 a b c d+3 b^2 c^2\right)+\frac{b d (2 a d+3 b c)}{x}\right)}{3 a b^2}-\frac{c^2 (b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{c x \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2}{a}","-\frac{d \sqrt{a+\frac{b}{x}} \left(2 \left(-2 a^2 d^2+9 a b c d+3 b^2 c^2\right)+\frac{b d (2 a d+3 b c)}{x}\right)}{3 a b^2}-\frac{c^2 (b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{c x \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2}{a}",1,"-(d*Sqrt[a + b/x]*(2*(3*b^2*c^2 + 9*a*b*c*d - 2*a^2*d^2) + (b*d*(3*b*c + 2*a*d))/x))/(3*a*b^2) + (c*Sqrt[a + b/x]*(c + d/x)^2*x)/a - (c^2*(b*c - 6*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(3/2)","A",5,5,21,0.2381,1,"{375, 98, 147, 63, 208}"
246,1,73,0,0.0540239,"\int \frac{\left(c+\frac{d}{x}\right)^2}{\sqrt{a+\frac{b}{x}}} \, dx","Int[(c + d/x)^2/Sqrt[a + b/x],x]","-\frac{c (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{c^2 x \sqrt{a+\frac{b}{x}}}{a}-\frac{2 d^2 \sqrt{a+\frac{b}{x}}}{b}","-\frac{c (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{c^2 x \sqrt{a+\frac{b}{x}}}{a}-\frac{2 d^2 \sqrt{a+\frac{b}{x}}}{b}",1,"(-2*d^2*Sqrt[a + b/x])/b + (c^2*Sqrt[a + b/x]*x)/a - (c*(b*c - 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(3/2)","A",5,5,21,0.2381,1,"{375, 89, 80, 63, 208}"
247,1,51,0,0.0331384,"\int \frac{c+\frac{d}{x}}{\sqrt{a+\frac{b}{x}}} \, dx","Int[(c + d/x)/Sqrt[a + b/x],x]","\frac{c x \sqrt{a+\frac{b}{x}}}{a}-\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{c x \sqrt{a+\frac{b}{x}}}{a}-\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}",1,"(c*Sqrt[a + b/x]*x)/a - ((b*c - 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(3/2)","A",4,4,19,0.2105,1,"{375, 78, 63, 208}"
248,1,43,0,0.0196423,"\int \frac{1}{\sqrt{a+\frac{b}{x}}} \, dx","Int[1/Sqrt[a + b/x],x]","\frac{x \sqrt{a+\frac{b}{x}}}{a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{x \sqrt{a+\frac{b}{x}}}{a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}",1,"(Sqrt[a + b/x]*x)/a - (b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(3/2)","A",4,4,11,0.3636,1,"{242, 51, 63, 208}"
249,1,108,0,0.0963475,"\int \frac{1}{\sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)} \, dx","Int[1/(Sqrt[a + b/x]*(c + d/x)),x]","-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2} c^2}-\frac{2 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 \sqrt{b c-a d}}+\frac{x \sqrt{a+\frac{b}{x}}}{a c}","-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2} c^2}-\frac{2 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 \sqrt{b c-a d}}+\frac{x \sqrt{a+\frac{b}{x}}}{a c}",1,"(Sqrt[a + b/x]*x)/(a*c) - (2*d^(3/2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^2*Sqrt[b*c - a*d]) - ((b*c + 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(3/2)*c^2)","A",7,6,21,0.2857,1,"{375, 103, 156, 63, 208, 205}"
250,1,172,0,0.2180575,"\int \frac{1}{\sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2} \, dx","Int[1/(Sqrt[a + b/x]*(c + d/x)^2),x]","-\frac{(4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2} c^3}-\frac{d^{3/2} (5 b c-4 a d) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 (b c-a d)^{3/2}}+\frac{d \sqrt{a+\frac{b}{x}} (b c-2 a d)}{a c^2 \left(c+\frac{d}{x}\right) (b c-a d)}+\frac{x \sqrt{a+\frac{b}{x}}}{a c \left(c+\frac{d}{x}\right)}","-\frac{(4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2} c^3}-\frac{d^{3/2} (5 b c-4 a d) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 (b c-a d)^{3/2}}+\frac{d \sqrt{a+\frac{b}{x}} (b c-2 a d)}{a c^2 \left(c+\frac{d}{x}\right) (b c-a d)}+\frac{x \sqrt{a+\frac{b}{x}}}{a c \left(c+\frac{d}{x}\right)}",1,"(d*(b*c - 2*a*d)*Sqrt[a + b/x])/(a*c^2*(b*c - a*d)*(c + d/x)) + (Sqrt[a + b/x]*x)/(a*c*(c + d/x)) - (d^(3/2)*(5*b*c - 4*a*d)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^3*(b*c - a*d)^(3/2)) - ((b*c + 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(3/2)*c^3)","A",8,7,21,0.3333,1,"{375, 103, 151, 156, 63, 208, 205}"
251,1,250,0,0.4000769,"\int \frac{1}{\sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^3} \, dx","Int[1/(Sqrt[a + b/x]*(c + d/x)^3),x]","-\frac{d^{3/2} \left(24 a^2 d^2-56 a b c d+35 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 (b c-a d)^{5/2}}-\frac{(6 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2} c^4}+\frac{d \sqrt{a+\frac{b}{x}} (b c-4 a d) (4 b c-3 a d)}{4 a c^3 \left(c+\frac{d}{x}\right) (b c-a d)^2}+\frac{d \sqrt{a+\frac{b}{x}} (2 b c-3 a d)}{2 a c^2 \left(c+\frac{d}{x}\right)^2 (b c-a d)}+\frac{x \sqrt{a+\frac{b}{x}}}{a c \left(c+\frac{d}{x}\right)^2}","-\frac{d^{3/2} \left(24 a^2 d^2-56 a b c d+35 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 (b c-a d)^{5/2}}-\frac{(6 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2} c^4}+\frac{d \sqrt{a+\frac{b}{x}} (b c-4 a d) (4 b c-3 a d)}{4 a c^3 \left(c+\frac{d}{x}\right) (b c-a d)^2}+\frac{d \sqrt{a+\frac{b}{x}} (2 b c-3 a d)}{2 a c^2 \left(c+\frac{d}{x}\right)^2 (b c-a d)}+\frac{x \sqrt{a+\frac{b}{x}}}{a c \left(c+\frac{d}{x}\right)^2}",1,"(d*(2*b*c - 3*a*d)*Sqrt[a + b/x])/(2*a*c^2*(b*c - a*d)*(c + d/x)^2) + (d*(b*c - 4*a*d)*(4*b*c - 3*a*d)*Sqrt[a + b/x])/(4*a*c^3*(b*c - a*d)^2*(c + d/x)) + (Sqrt[a + b/x]*x)/(a*c*(c + d/x)^2) - (d^(3/2)*(35*b^2*c^2 - 56*a*b*c*d + 24*a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(4*c^4*(b*c - a*d)^(5/2)) - ((b*c + 6*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(3/2)*c^4)","A",9,7,21,0.3333,1,"{375, 103, 151, 156, 63, 208, 205}"
252,1,132,0,0.1012601,"\int \frac{\left(c+\frac{d}{x}\right)^3}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[(c + d/x)^3/(a + b/x)^(3/2),x]","\frac{(b c-2 a d) \left(2 a^2 d^2-2 a b c d+3 b^2 c^2\right)-\frac{a b d^2 (2 a d+b c)}{x}}{a^2 b^2 \sqrt{a+\frac{b}{x}}}-\frac{3 c^2 (b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{c x \left(c+\frac{d}{x}\right)^2}{a \sqrt{a+\frac{b}{x}}}","\frac{(b c-2 a d) \left(2 a^2 d^2-2 a b c d+3 b^2 c^2\right)-\frac{a b d^2 (2 a d+b c)}{x}}{a^2 b^2 \sqrt{a+\frac{b}{x}}}-\frac{3 c^2 (b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{c x \left(c+\frac{d}{x}\right)^2}{a \sqrt{a+\frac{b}{x}}}",1,"((b*c - 2*a*d)*(3*b^2*c^2 - 2*a*b*c*d + 2*a^2*d^2) - (a*b*d^2*(b*c + 2*a*d))/x)/(a^2*b^2*Sqrt[a + b/x]) + (c*(c + d/x)^2*x)/(a*Sqrt[a + b/x]) - (3*c^2*(b*c - 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(5/2)","A",5,5,21,0.2381,1,"{375, 98, 146, 63, 208}"
253,1,90,0,0.0787857,"\int \frac{\left(c+\frac{d}{x}\right)^2}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[(c + d/x)^2/(a + b/x)^(3/2),x]","\frac{\frac{c (3 b c-4 a d)}{a^2}+\frac{2 d^2}{b}}{\sqrt{a+\frac{b}{x}}}-\frac{c (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{c^2 x}{a \sqrt{a+\frac{b}{x}}}","\frac{2 a^2 d^2+b c (3 b c-4 a d)}{a^2 b \sqrt{a+\frac{b}{x}}}-\frac{c (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{c^2 x}{a \sqrt{a+\frac{b}{x}}}",1,"((2*d^2)/b + (c*(3*b*c - 4*a*d))/a^2)/Sqrt[a + b/x] + (c^2*x)/(a*Sqrt[a + b/x]) - (c*(3*b*c - 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(5/2)","A",5,5,21,0.2381,1,"{375, 89, 78, 63, 208}"
254,1,76,0,0.050474,"\int \frac{c+\frac{d}{x}}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[(c + d/x)/(a + b/x)^(3/2),x]","\frac{3 b c-2 a d}{a^2 \sqrt{a+\frac{b}{x}}}-\frac{(3 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{c x}{a \sqrt{a+\frac{b}{x}}}","\frac{3 b c-2 a d}{a^2 \sqrt{a+\frac{b}{x}}}-\frac{(3 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{c x}{a \sqrt{a+\frac{b}{x}}}",1,"(3*b*c - 2*a*d)/(a^2*Sqrt[a + b/x]) + (c*x)/(a*Sqrt[a + b/x]) - ((3*b*c - 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(5/2)","A",5,5,19,0.2632,1,"{375, 78, 51, 63, 208}"
255,1,61,0,0.0306506,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[(a + b/x)^(-3/2),x]","\frac{3 x \sqrt{a+\frac{b}{x}}}{a^2}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2 x}{a \sqrt{a+\frac{b}{x}}}","\frac{3 b}{a^2 \sqrt{a+\frac{b}{x}}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{x}{a \sqrt{a+\frac{b}{x}}}",1,"(-2*x)/(a*Sqrt[a + b/x]) + (3*Sqrt[a + b/x]*x)/a^2 - (3*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(5/2)","A",5,4,11,0.3636,1,"{242, 51, 63, 208}"
256,1,147,0,0.1940212,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)} \, dx","Int[1/((a + b/x)^(3/2)*(c + d/x)),x]","-\frac{(2 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2} c^2}+\frac{b (3 b c-a d)}{a^2 c \sqrt{a+\frac{b}{x}} (b c-a d)}+\frac{2 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 (b c-a d)^{3/2}}+\frac{x}{a c \sqrt{a+\frac{b}{x}}}","-\frac{(2 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2} c^2}+\frac{b (3 b c-a d)}{a^2 c \sqrt{a+\frac{b}{x}} (b c-a d)}+\frac{2 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 (b c-a d)^{3/2}}+\frac{x}{a c \sqrt{a+\frac{b}{x}}}",1,"(b*(3*b*c - a*d))/(a^2*c*(b*c - a*d)*Sqrt[a + b/x]) + x/(a*c*Sqrt[a + b/x]) + (2*d^(5/2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^2*(b*c - a*d)^(3/2)) - ((3*b*c + 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(5/2)*c^2)","A",8,7,21,0.3333,1,"{375, 103, 152, 156, 63, 208, 205}"
257,1,224,0,0.3226931,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^2} \, dx","Int[1/((a + b/x)^(3/2)*(c + d/x)^2),x]","\frac{b \left(2 a^2 d^2-2 a b c d+3 b^2 c^2\right)}{a^2 c^2 \sqrt{a+\frac{b}{x}} (b c-a d)^2}-\frac{(4 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2} c^3}+\frac{d^{5/2} (7 b c-4 a d) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 (b c-a d)^{5/2}}+\frac{d (b c-2 a d)}{a c^2 \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right) (b c-a d)}+\frac{x}{a c \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)}","\frac{b \left(2 a^2 d^2-2 a b c d+3 b^2 c^2\right)}{a^2 c^2 \sqrt{a+\frac{b}{x}} (b c-a d)^2}-\frac{(4 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2} c^3}+\frac{d^{5/2} (7 b c-4 a d) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 (b c-a d)^{5/2}}+\frac{d (b c-2 a d)}{a c^2 \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right) (b c-a d)}+\frac{x}{a c \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)}",1,"(b*(3*b^2*c^2 - 2*a*b*c*d + 2*a^2*d^2))/(a^2*c^2*(b*c - a*d)^2*Sqrt[a + b/x]) + (d*(b*c - 2*a*d))/(a*c^2*(b*c - a*d)*Sqrt[a + b/x]*(c + d/x)) + x/(a*c*Sqrt[a + b/x]*(c + d/x)) + (d^(5/2)*(7*b*c - 4*a*d)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^3*(b*c - a*d)^(5/2)) - ((3*b*c + 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(5/2)*c^3)","A",9,8,21,0.3810,1,"{375, 103, 151, 152, 156, 63, 208, 205}"
258,1,320,0,0.5249759,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^3} \, dx","Int[1/((a + b/x)^(3/2)*(c + d/x)^3),x]","\frac{d \left(12 a^2 d^2-21 a b c d+4 b^2 c^2\right)}{4 a c^3 \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right) (b c-a d)^2}+\frac{3 b (2 b c-a d) \left(4 a^2 d^2-a b c d+2 b^2 c^2\right)}{4 a^2 c^3 \sqrt{a+\frac{b}{x}} (b c-a d)^3}+\frac{3 d^{5/2} \left(8 a^2 d^2-24 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 (b c-a d)^{7/2}}-\frac{3 (2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2} c^4}+\frac{d (2 b c-3 a d)}{2 a c^2 \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2 (b c-a d)}+\frac{x}{a c \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2}","\frac{d \left(12 a^2 d^2-21 a b c d+4 b^2 c^2\right)}{4 a c^3 \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right) (b c-a d)^2}+\frac{3 b (2 b c-a d) \left(4 a^2 d^2-a b c d+2 b^2 c^2\right)}{4 a^2 c^3 \sqrt{a+\frac{b}{x}} (b c-a d)^3}+\frac{3 d^{5/2} \left(8 a^2 d^2-24 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 (b c-a d)^{7/2}}-\frac{3 (2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2} c^4}+\frac{d (2 b c-3 a d)}{2 a c^2 \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2 (b c-a d)}+\frac{x}{a c \sqrt{a+\frac{b}{x}} \left(c+\frac{d}{x}\right)^2}",1,"(3*b*(2*b*c - a*d)*(2*b^2*c^2 - a*b*c*d + 4*a^2*d^2))/(4*a^2*c^3*(b*c - a*d)^3*Sqrt[a + b/x]) + (d*(2*b*c - 3*a*d))/(2*a*c^2*(b*c - a*d)*Sqrt[a + b/x]*(c + d/x)^2) + (d*(4*b^2*c^2 - 21*a*b*c*d + 12*a^2*d^2))/(4*a*c^3*(b*c - a*d)^2*Sqrt[a + b/x]*(c + d/x)) + x/(a*c*Sqrt[a + b/x]*(c + d/x)^2) + (3*d^(5/2)*(21*b^2*c^2 - 24*a*b*c*d + 8*a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(4*c^4*(b*c - a*d)^(7/2)) - (3*(b*c + 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(5/2)*c^4)","A",10,8,21,0.3810,1,"{375, 103, 151, 152, 156, 63, 208, 205}"
259,1,143,0,0.1512273,"\int \frac{\left(c+\frac{d}{x}\right)^3}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[(c + d/x)^3/(a + b/x)^(5/2),x]","\frac{(b c-a d) \left(-2 a^2 b d (5 c x+3 d)-4 a^3 d^2 x+a b^2 c (20 c x-3 d)+15 b^3 c^2\right)}{3 a^3 b^2 x \left(a+\frac{b}{x}\right)^{3/2}}-\frac{c^2 (5 b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{c x \left(c+\frac{d}{x}\right)^2}{a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{(b c-a d) \left(-2 a^2 b d (5 c x+3 d)-4 a^3 d^2 x+a b^2 c (20 c x-3 d)+15 b^3 c^2\right)}{3 a^3 b^2 x \left(a+\frac{b}{x}\right)^{3/2}}-\frac{c^2 (5 b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{c x \left(c+\frac{d}{x}\right)^2}{a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(c*(c + d/x)^2*x)/(a*(a + b/x)^(3/2)) + ((b*c - a*d)*(15*b^3*c^2 - 4*a^3*d^2*x - 2*a^2*b*d*(3*d + 5*c*x) + a*b^2*c*(-3*d + 20*c*x)))/(3*a^3*b^2*(a + b/x)^(3/2)*x) - (c^2*(5*b*c - 6*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(7/2)","A",5,5,21,0.2381,1,"{375, 98, 145, 63, 208}"
260,1,118,0,0.0951476,"\int \frac{\left(c+\frac{d}{x}\right)^2}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[(c + d/x)^2/(a + b/x)^(5/2),x]","\frac{\frac{c (5 b c-4 a d)}{a^2}+\frac{2 d^2}{b}}{3 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{c (5 b c-4 a d)}{a^3 \sqrt{a+\frac{b}{x}}}-\frac{c (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{c^2 x}{a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{2 a^2 d^2+b c (5 b c-4 a d)}{3 a^2 b \left(a+\frac{b}{x}\right)^{3/2}}+\frac{c (5 b c-4 a d)}{a^3 \sqrt{a+\frac{b}{x}}}-\frac{c (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{c^2 x}{a \left(a+\frac{b}{x}\right)^{3/2}}",1,"((2*d^2)/b + (c*(5*b*c - 4*a*d))/a^2)/(3*(a + b/x)^(3/2)) + (c*(5*b*c - 4*a*d))/(a^3*Sqrt[a + b/x]) + (c^2*x)/(a*(a + b/x)^(3/2)) - (c*(5*b*c - 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(7/2)","A",6,6,21,0.2857,1,"{375, 89, 78, 51, 63, 208}"
261,1,103,0,0.0654625,"\int \frac{c+\frac{d}{x}}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[(c + d/x)/(a + b/x)^(5/2),x]","\frac{5 b c-2 a d}{a^3 \sqrt{a+\frac{b}{x}}}+\frac{5 b c-2 a d}{3 a^2 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{(5 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{c x}{a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{5 b c-2 a d}{a^3 \sqrt{a+\frac{b}{x}}}+\frac{5 b c-2 a d}{3 a^2 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{(5 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{c x}{a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(5*b*c - 2*a*d)/(3*a^2*(a + b/x)^(3/2)) + (5*b*c - 2*a*d)/(a^3*Sqrt[a + b/x]) + (c*x)/(a*(a + b/x)^(3/2)) - ((5*b*c - 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(7/2)","A",6,5,19,0.2632,1,"{375, 78, 51, 63, 208}"
262,1,82,0,0.0377736,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[(a + b/x)^(-5/2),x]","\frac{5 x \sqrt{a+\frac{b}{x}}}{a^3}-\frac{10 x}{3 a^2 \sqrt{a+\frac{b}{x}}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{2 x}{3 a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{5 b}{a^3 \sqrt{a+\frac{b}{x}}}+\frac{5 b}{3 a^2 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{x}{a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-2*x)/(3*a*(a + b/x)^(3/2)) - (10*x)/(3*a^2*Sqrt[a + b/x]) + (5*Sqrt[a + b/x]*x)/a^3 - (5*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(7/2)","A",6,4,11,0.3636,1,"{242, 51, 63, 208}"
263,1,201,0,0.315132,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)} \, dx","Int[1/((a + b/x)^(5/2)*(c + d/x)),x]","\frac{b \left(a^2 d^2-8 a b c d+5 b^2 c^2\right)}{a^3 c \sqrt{a+\frac{b}{x}} (b c-a d)^2}-\frac{(2 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2} c^2}+\frac{b (5 b c-3 a d)}{3 a^2 c \left(a+\frac{b}{x}\right)^{3/2} (b c-a d)}-\frac{2 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 (b c-a d)^{5/2}}+\frac{x}{a c \left(a+\frac{b}{x}\right)^{3/2}}","\frac{b \left(a^2 d^2-8 a b c d+5 b^2 c^2\right)}{a^3 c \sqrt{a+\frac{b}{x}} (b c-a d)^2}-\frac{(2 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2} c^2}+\frac{b (5 b c-3 a d)}{3 a^2 c \left(a+\frac{b}{x}\right)^{3/2} (b c-a d)}-\frac{2 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^2 (b c-a d)^{5/2}}+\frac{x}{a c \left(a+\frac{b}{x}\right)^{3/2}}",1,"(b*(5*b*c - 3*a*d))/(3*a^2*c*(b*c - a*d)*(a + b/x)^(3/2)) + (b*(5*b^2*c^2 - 8*a*b*c*d + a^2*d^2))/(a^3*c*(b*c - a*d)^2*Sqrt[a + b/x]) + x/(a*c*(a + b/x)^(3/2)) - (2*d^(7/2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^2*(b*c - a*d)^(5/2)) - ((5*b*c + 2*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(7/2)*c^2)","A",9,7,21,0.3333,1,"{375, 103, 152, 156, 63, 208, 205}"
264,1,287,0,0.4477131,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)^2} \, dx","Int[1/((a + b/x)^(5/2)*(c + d/x)^2),x]","\frac{b (b c-2 a d) \left(a^2 d^2-a b c d+5 b^2 c^2\right)}{a^3 c^2 \sqrt{a+\frac{b}{x}} (b c-a d)^3}+\frac{b \left(6 a^2 d^2-6 a b c d+5 b^2 c^2\right)}{3 a^2 c^2 \left(a+\frac{b}{x}\right)^{3/2} (b c-a d)^2}-\frac{(4 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2} c^3}-\frac{d^{7/2} (9 b c-4 a d) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 (b c-a d)^{7/2}}+\frac{d (b c-2 a d)}{a c^2 \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right) (b c-a d)}+\frac{x}{a c \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)}","\frac{b (b c-2 a d) \left(a^2 d^2-a b c d+5 b^2 c^2\right)}{a^3 c^2 \sqrt{a+\frac{b}{x}} (b c-a d)^3}+\frac{b \left(6 a^2 d^2-6 a b c d+5 b^2 c^2\right)}{3 a^2 c^2 \left(a+\frac{b}{x}\right)^{3/2} (b c-a d)^2}-\frac{(4 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2} c^3}-\frac{d^{7/2} (9 b c-4 a d) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{c^3 (b c-a d)^{7/2}}+\frac{d (b c-2 a d)}{a c^2 \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right) (b c-a d)}+\frac{x}{a c \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)}",1,"(b*(5*b^2*c^2 - 6*a*b*c*d + 6*a^2*d^2))/(3*a^2*c^2*(b*c - a*d)^2*(a + b/x)^(3/2)) + (b*(b*c - 2*a*d)*(5*b^2*c^2 - a*b*c*d + a^2*d^2))/(a^3*c^2*(b*c - a*d)^3*Sqrt[a + b/x]) + (d*(b*c - 2*a*d))/(a*c^2*(b*c - a*d)*(a + b/x)^(3/2)*(c + d/x)) + x/(a*c*(a + b/x)^(3/2)*(c + d/x)) - (d^(7/2)*(9*b*c - 4*a*d)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(c^3*(b*c - a*d)^(7/2)) - ((5*b*c + 4*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(7/2)*c^3)","A",10,8,21,0.3810,1,"{375, 103, 151, 152, 156, 63, 208, 205}"
265,1,409,0,0.7024139,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} \left(c+\frac{d}{x}\right)^3} \, dx","Int[1/((a + b/x)^(5/2)*(c + d/x)^3),x]","\frac{d \left(12 a^2 d^2-23 a b c d+4 b^2 c^2\right)}{4 a c^3 \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right) (b c-a d)^2}+\frac{b \left(24 a^2 b^2 c^2 d^2-35 a^3 b c d^3+12 a^4 d^4-56 a b^3 c^3 d+20 b^4 c^4\right)}{4 a^3 c^3 \sqrt{a+\frac{b}{x}} (b c-a d)^4}+\frac{b \left(87 a^2 b c d^2-36 a^3 d^3-36 a b^2 c^2 d+20 b^3 c^3\right)}{12 a^2 c^3 \left(a+\frac{b}{x}\right)^{3/2} (b c-a d)^3}-\frac{d^{7/2} \left(24 a^2 d^2-88 a b c d+99 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 (b c-a d)^{9/2}}-\frac{(6 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2} c^4}+\frac{d (2 b c-3 a d)}{2 a c^2 \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^2 (b c-a d)}+\frac{x}{a c \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^2}","\frac{d \left(12 a^2 d^2-23 a b c d+4 b^2 c^2\right)}{4 a c^3 \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right) (b c-a d)^2}+\frac{b \left(24 a^2 b^2 c^2 d^2-35 a^3 b c d^3+12 a^4 d^4-56 a b^3 c^3 d+20 b^4 c^4\right)}{4 a^3 c^3 \sqrt{a+\frac{b}{x}} (b c-a d)^4}+\frac{b \left(87 a^2 b c d^2-36 a^3 d^3-36 a b^2 c^2 d+20 b^3 c^3\right)}{12 a^2 c^3 \left(a+\frac{b}{x}\right)^{3/2} (b c-a d)^3}-\frac{d^{7/2} \left(24 a^2 d^2-88 a b c d+99 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b c-a d}}\right)}{4 c^4 (b c-a d)^{9/2}}-\frac{(6 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2} c^4}+\frac{d (2 b c-3 a d)}{2 a c^2 \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^2 (b c-a d)}+\frac{x}{a c \left(a+\frac{b}{x}\right)^{3/2} \left(c+\frac{d}{x}\right)^2}",1,"(b*(20*b^3*c^3 - 36*a*b^2*c^2*d + 87*a^2*b*c*d^2 - 36*a^3*d^3))/(12*a^2*c^3*(b*c - a*d)^3*(a + b/x)^(3/2)) + (b*(20*b^4*c^4 - 56*a*b^3*c^3*d + 24*a^2*b^2*c^2*d^2 - 35*a^3*b*c*d^3 + 12*a^4*d^4))/(4*a^3*c^3*(b*c - a*d)^4*Sqrt[a + b/x]) + (d*(2*b*c - 3*a*d))/(2*a*c^2*(b*c - a*d)*(a + b/x)^(3/2)*(c + d/x)^2) + (d*(4*b^2*c^2 - 23*a*b*c*d + 12*a^2*d^2))/(4*a*c^3*(b*c - a*d)^2*(a + b/x)^(3/2)*(c + d/x)) + x/(a*c*(a + b/x)^(3/2)*(c + d/x)^2) - (d^(7/2)*(99*b^2*c^2 - 88*a*b*c*d + 24*a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[a + b/x])/Sqrt[b*c - a*d]])/(4*c^4*(b*c - a*d)^(9/2)) - ((5*b*c + 6*a*d)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(a^(7/2)*c^4)","A",11,8,21,0.3810,1,"{375, 103, 151, 152, 156, 63, 208, 205}"
266,1,123,0,0.0938878,"\int \sqrt{a+\frac{b}{x}} \sqrt{c+\frac{d}{x}} \, dx","Int[Sqrt[a + b/x]*Sqrt[c + d/x],x]","x \sqrt{a+\frac{b}{x}} \sqrt{c+\frac{d}{x}}+\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+\frac{b}{x}}}{\sqrt{a} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{a} \sqrt{c}}-2 \sqrt{b} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b} \sqrt{c+\frac{d}{x}}}\right)","x \sqrt{a+\frac{b}{x}} \sqrt{c+\frac{d}{x}}+\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+\frac{b}{x}}}{\sqrt{a} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{a} \sqrt{c}}-2 \sqrt{b} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b} \sqrt{c+\frac{d}{x}}}\right)",1,"Sqrt[a + b/x]*Sqrt[c + d/x]*x + ((b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b/x])/(Sqrt[a]*Sqrt[c + d/x])])/(Sqrt[a]*Sqrt[c]) - 2*Sqrt[b]*Sqrt[d]*ArcTanh[(Sqrt[d]*Sqrt[a + b/x])/(Sqrt[b]*Sqrt[c + d/x])]","A",8,8,23,0.3478,1,"{375, 97, 157, 63, 217, 206, 93, 208}"
267,1,81,0,0.0520053,"\int \frac{\sqrt{a+\frac{b}{x}}}{\sqrt{c+\frac{d}{x}}} \, dx","Int[Sqrt[a + b/x]/Sqrt[c + d/x],x]","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+\frac{b}{x}}}{\sqrt{a} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{a} c^{3/2}}+\frac{x \sqrt{a+\frac{b}{x}} \sqrt{c+\frac{d}{x}}}{c}","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+\frac{b}{x}}}{\sqrt{a} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{a} c^{3/2}}+\frac{x \sqrt{a+\frac{b}{x}} \sqrt{c+\frac{d}{x}}}{c}",1,"(Sqrt[a + b/x]*Sqrt[c + d/x]*x)/c + ((b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b/x])/(Sqrt[a]*Sqrt[c + d/x])])/(Sqrt[a]*c^(3/2))","A",4,4,23,0.1739,1,"{375, 94, 93, 208}"
268,1,122,0,0.0803529,"\int \frac{\sqrt{a+\frac{b}{x}}}{\left(c+\frac{d}{x}\right)^{3/2}} \, dx","Int[Sqrt[a + b/x]/(c + d/x)^(3/2),x]","-\frac{\sqrt{a+\frac{b}{x}} (b c-3 a d)}{a c^2 \sqrt{c+\frac{d}{x}}}+\frac{(b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+\frac{b}{x}}}{\sqrt{a} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{a} c^{5/2}}+\frac{x \left(a+\frac{b}{x}\right)^{3/2}}{a c \sqrt{c+\frac{d}{x}}}","-\frac{\sqrt{a+\frac{b}{x}} (b c-3 a d)}{a c^2 \sqrt{c+\frac{d}{x}}}+\frac{(b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+\frac{b}{x}}}{\sqrt{a} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{a} c^{5/2}}+\frac{x \left(a+\frac{b}{x}\right)^{3/2}}{a c \sqrt{c+\frac{d}{x}}}",1,"-(((b*c - 3*a*d)*Sqrt[a + b/x])/(a*c^2*Sqrt[c + d/x])) + ((a + b/x)^(3/2)*x)/(a*c*Sqrt[c + d/x]) + ((b*c - 3*a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b/x])/(Sqrt[a]*Sqrt[c + d/x])])/(Sqrt[a]*c^(5/2))","A",5,5,23,0.2174,1,"{375, 96, 94, 93, 208}"
269,1,96,0,0.0605418,"\int \left(a+\frac{b}{x}\right)^p \left(c+\frac{d}{x}\right)^q \, dx","Int[(a + b/x)^p*(c + d/x)^q,x]","-\frac{b \left(a+\frac{b}{x}\right)^{p+1} \left(c+\frac{d}{x}\right)^q \left(\frac{b \left(c+\frac{d}{x}\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,2;p+2;-\frac{d \left(a+\frac{b}{x}\right)}{b c-a d},\frac{a+\frac{b}{x}}{a}\right)}{a^2 (p+1)}","-\frac{b \left(a+\frac{b}{x}\right)^{p+1} \left(c+\frac{d}{x}\right)^q \left(\frac{b \left(c+\frac{d}{x}\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,2;p+2;-\frac{d \left(a+\frac{b}{x}\right)}{b c-a d},\frac{a+\frac{b}{x}}{a}\right)}{a^2 (p+1)}",1,"-((b*(a + b/x)^(1 + p)*(c + d/x)^q*AppellF1[1 + p, -q, 2, 2 + p, -((d*(a + b/x))/(b*c - a*d)), (a + b/x)/a])/(a^2*(1 + p)*((b*(c + d/x))/(b*c - a*d))^q))","A",3,3,19,0.1579,1,"{375, 137, 136}"
270,1,39,0,0.0200836,"\int \frac{a+\frac{b}{x^2}}{c+\frac{d}{x^2}} \, dx","Int[(a + b/x^2)/(c + d/x^2),x]","\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)}{c^{3/2} \sqrt{d}}+\frac{a x}{c}","\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)}{c^{3/2} \sqrt{d}}+\frac{a x}{c}",1,"(a*x)/c + ((b*c - a*d)*ArcTan[(Sqrt[c]*x)/Sqrt[d]])/(c^(3/2)*Sqrt[d])","A",3,3,17,0.1765,1,"{374, 388, 205}"
271,1,233,0,0.2175788,"\int \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}} \, dx","Int[Sqrt[a + b/x^2]*Sqrt[c + d/x^2],x]","-\frac{2 d \sqrt{a+\frac{b}{x^2}}}{x \sqrt{c+\frac{d}{x^2}}}+x \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}}-\frac{\sqrt{c} \sqrt{a+\frac{b}{x^2}} (a d+b c) F\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}+\frac{2 \sqrt{c} \sqrt{d} \sqrt{a+\frac{b}{x^2}} E\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}","-\frac{2 d \sqrt{a+\frac{b}{x^2}}}{x \sqrt{c+\frac{d}{x^2}}}+x \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}}-\frac{\sqrt{c} \sqrt{a+\frac{b}{x^2}} (a d+b c) F\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}+\frac{2 \sqrt{c} \sqrt{d} \sqrt{a+\frac{b}{x^2}} E\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}",1,"(-2*d*Sqrt[a + b/x^2])/(Sqrt[c + d/x^2]*x) + Sqrt[a + b/x^2]*Sqrt[c + d/x^2]*x + (2*Sqrt[c]*Sqrt[d]*Sqrt[a + b/x^2]*EllipticE[ArcCot[(Sqrt[c]*x)/Sqrt[d]], 1 - (b*c)/(a*d)])/(Sqrt[(c*(a + b/x^2))/(a*(c + d/x^2))]*Sqrt[c + d/x^2]) - (Sqrt[c]*(b*c + a*d)*Sqrt[a + b/x^2]*EllipticF[ArcCot[(Sqrt[c]*x)/Sqrt[d]], 1 - (b*c)/(a*d)])/(a*Sqrt[d]*Sqrt[(c*(a + b/x^2))/(a*(c + d/x^2))]*Sqrt[c + d/x^2])","A",6,6,23,0.2609,1,"{375, 473, 531, 418, 492, 411}"
272,1,232,0,0.2047257,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{c+\frac{d}{x^2}}} \, dx","Int[Sqrt[a + b/x^2]/Sqrt[c + d/x^2],x]","-\frac{d \sqrt{a+\frac{b}{x^2}}}{c x \sqrt{c+\frac{d}{x^2}}}+\frac{x \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}}}{c}-\frac{b \sqrt{c} \sqrt{a+\frac{b}{x^2}} F\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}+\frac{\sqrt{d} \sqrt{a+\frac{b}{x^2}} E\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}","-\frac{d \sqrt{a+\frac{b}{x^2}}}{c x \sqrt{c+\frac{d}{x^2}}}+\frac{x \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}}}{c}-\frac{b \sqrt{c} \sqrt{a+\frac{b}{x^2}} F\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}+\frac{\sqrt{d} \sqrt{a+\frac{b}{x^2}} E\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}",1,"-((d*Sqrt[a + b/x^2])/(c*Sqrt[c + d/x^2]*x)) + (Sqrt[a + b/x^2]*Sqrt[c + d/x^2]*x)/c + (Sqrt[d]*Sqrt[a + b/x^2]*EllipticE[ArcCot[(Sqrt[c]*x)/Sqrt[d]], 1 - (b*c)/(a*d)])/(Sqrt[c]*Sqrt[(c*(a + b/x^2))/(a*(c + d/x^2))]*Sqrt[c + d/x^2]) - (b*Sqrt[c]*Sqrt[a + b/x^2]*EllipticF[ArcCot[(Sqrt[c]*x)/Sqrt[d]], 1 - (b*c)/(a*d)])/(a*Sqrt[d]*Sqrt[(c*(a + b/x^2))/(a*(c + d/x^2))]*Sqrt[c + d/x^2])","A",7,7,23,0.3043,1,"{375, 475, 21, 422, 418, 492, 411}"
273,1,262,0,0.2801292,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{\left(c+\frac{d}{x^2}\right)^{3/2}} \, dx","Int[Sqrt[a + b/x^2]/(c + d/x^2)^(3/2),x]","-\frac{2 d \sqrt{a+\frac{b}{x^2}}}{c^2 x \sqrt{c+\frac{d}{x^2}}}+\frac{2 x \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}}}{c^2}+\frac{2 \sqrt{d} \sqrt{a+\frac{b}{x^2}} E\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{c^{3/2} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}-\frac{x \sqrt{a+\frac{b}{x^2}}}{c \sqrt{c+\frac{d}{x^2}}}-\frac{b \sqrt{a+\frac{b}{x^2}} F\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{c} \sqrt{d} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}","-\frac{2 d \sqrt{a+\frac{b}{x^2}}}{c^2 x \sqrt{c+\frac{d}{x^2}}}+\frac{2 x \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}}}{c^2}+\frac{2 \sqrt{d} \sqrt{a+\frac{b}{x^2}} E\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{c^{3/2} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}-\frac{x \sqrt{a+\frac{b}{x^2}}}{c \sqrt{c+\frac{d}{x^2}}}-\frac{b \sqrt{a+\frac{b}{x^2}} F\left(\cot ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{c} \sqrt{d} \sqrt{c+\frac{d}{x^2}} \sqrt{\frac{c \left(a+\frac{b}{x^2}\right)}{a \left(c+\frac{d}{x^2}\right)}}}",1,"(-2*d*Sqrt[a + b/x^2])/(c^2*Sqrt[c + d/x^2]*x) - (Sqrt[a + b/x^2]*x)/(c*Sqrt[c + d/x^2]) + (2*Sqrt[a + b/x^2]*Sqrt[c + d/x^2]*x)/c^2 + (2*Sqrt[d]*Sqrt[a + b/x^2]*EllipticE[ArcCot[(Sqrt[c]*x)/Sqrt[d]], 1 - (b*c)/(a*d)])/(c^(3/2)*Sqrt[(c*(a + b/x^2))/(a*(c + d/x^2))]*Sqrt[c + d/x^2]) - (b*Sqrt[a + b/x^2]*EllipticF[ArcCot[(Sqrt[c]*x)/Sqrt[d]], 1 - (b*c)/(a*d)])/(a*Sqrt[c]*Sqrt[d]*Sqrt[(c*(a + b/x^2))/(a*(c + d/x^2))]*Sqrt[c + d/x^2])","A",7,7,23,0.3043,1,"{375, 469, 583, 531, 418, 492, 411}"
274,1,79,0,0.0883045,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q,x]","x \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{1}{2};-p,-q;\frac{1}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)","x \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{1}{2};-p,-q;\frac{1}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)",1,"((a + b/x^2)^p*(c + d/x^2)^q*x*AppellF1[-1/2, -p, -q, 1/2, -(b/(a*x^2)), -(d/(c*x^2))])/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,19,0.1579,1,"{375, 511, 510}"
275,1,145,0,0.1056087,"\int \frac{a+\frac{b}{x^3}}{c+\frac{d}{x^3}} \, dx","Int[(a + b/x^3)/(c + d/x^3),x]","-\frac{(b c-a d) \log \left(c^{2/3} x^2-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3}\right)}{6 c^{4/3} d^{2/3}}+\frac{(b c-a d) \log \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{3 c^{4/3} d^{2/3}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{c} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} c^{4/3} d^{2/3}}+\frac{a x}{c}","-\frac{(b c-a d) \log \left(c^{2/3} x^2-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3}\right)}{6 c^{4/3} d^{2/3}}+\frac{(b c-a d) \log \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{3 c^{4/3} d^{2/3}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{c} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} c^{4/3} d^{2/3}}+\frac{a x}{c}",1,"(a*x)/c - ((b*c - a*d)*ArcTan[(d^(1/3) - 2*c^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*c^(4/3)*d^(2/3)) + ((b*c - a*d)*Log[d^(1/3) + c^(1/3)*x])/(3*c^(4/3)*d^(2/3)) - ((b*c - a*d)*Log[d^(2/3) - c^(1/3)*d^(1/3)*x + c^(2/3)*x^2])/(6*c^(4/3)*d^(2/3))","A",8,8,17,0.4706,1,"{374, 388, 200, 31, 634, 617, 204, 628}"
276,1,49,0,0.0487507,"\int \frac{a+b \sqrt{x}}{c+d \sqrt{x}} \, dx","Int[(a + b*Sqrt[x])/(c + d*Sqrt[x]),x]","-\frac{2 \sqrt{x} (b c-a d)}{d^2}+\frac{2 c (b c-a d) \log \left(c+d \sqrt{x}\right)}{d^3}+\frac{b x}{d}","-\frac{2 \sqrt{x} (b c-a d)}{d^2}+\frac{2 c (b c-a d) \log \left(c+d \sqrt{x}\right)}{d^3}+\frac{b x}{d}",1,"(-2*(b*c - a*d)*Sqrt[x])/d^2 + (b*x)/d + (2*c*(b*c - a*d)*Log[c + d*Sqrt[x]])/d^3","A",3,2,21,0.09524,1,"{376, 77}"
277,1,26,0,0.0159524,"\int \frac{-1+\sqrt[3]{x}}{1+\sqrt[3]{x}} \, dx","Int[(-1 + x^(1/3))/(1 + x^(1/3)),x]","-3 x^{2/3}+x+6 \sqrt[3]{x}-6 \log \left(\sqrt[3]{x}+1\right)","-3 x^{2/3}+x+6 \sqrt[3]{x}-6 \log \left(\sqrt[3]{x}+1\right)",1,"6*x^(1/3) - 3*x^(2/3) + x - 6*Log[1 + x^(1/3)]","A",3,2,17,0.1176,1,"{376, 77}"
278,1,17,0,0.0146946,"\int \frac{1+x^{2/3}}{-1+x^{2/3}} \, dx","Int[(1 + x^(2/3))/(-1 + x^(2/3)),x]","x+6 \sqrt[3]{x}-6 \tanh ^{-1}\left(\sqrt[3]{x}\right)","x+6 \sqrt[3]{x}-6 \tanh ^{-1}\left(\sqrt[3]{x}\right)",1,"6*x^(1/3) + x - 6*ArcTanh[x^(1/3)]","A",4,4,17,0.2353,1,"{376, 459, 321, 207}"
279,1,104,0,0.0861164,"\int \frac{-16+x^{3/4}}{16+x^{3/4}} \, dx","Int[(-16 + x^(3/4))/(16 + x^(3/4)),x]","x-128 \sqrt[4]{x}+\frac{256}{3} \sqrt[3]{2} \log \left(\sqrt[4]{x}+2 \sqrt[3]{2}\right)-\frac{128}{3} \sqrt[3]{2} \log \left(\sqrt{x}-2 \sqrt[3]{2} \sqrt[4]{x}+4\ 2^{2/3}\right)-\frac{256 \sqrt[3]{2} \tan ^{-1}\left(\frac{\sqrt[3]{2}-\sqrt[4]{x}}{\sqrt[3]{2} \sqrt{3}}\right)}{\sqrt{3}}","x-128 \sqrt[4]{x}+\frac{256}{3} \sqrt[3]{2} \log \left(\sqrt[4]{x}+2 \sqrt[3]{2}\right)-\frac{128}{3} \sqrt[3]{2} \log \left(\sqrt{x}-2 \sqrt[3]{2} \sqrt[4]{x}+4\ 2^{2/3}\right)-\frac{256 \sqrt[3]{2} \tan ^{-1}\left(\frac{\sqrt[3]{2}-\sqrt[4]{x}}{\sqrt[3]{2} \sqrt{3}}\right)}{\sqrt{3}}",1,"-128*x^(1/4) + x - (256*2^(1/3)*ArcTan[(2^(1/3) - x^(1/4))/(2^(1/3)*Sqrt[3])])/Sqrt[3] + (256*2^(1/3)*Log[2*2^(1/3) + x^(1/4)])/3 - (128*2^(1/3)*Log[4*2^(2/3) - 2*2^(1/3)*x^(1/4) + Sqrt[x]])/3","A",9,9,17,0.5294,1,"{376, 459, 321, 200, 31, 634, 617, 204, 628}"
280,1,30,0,0.0185796,"\int \frac{1+\frac{1}{\sqrt[3]{x}}}{-1+\frac{1}{\sqrt[3]{x}}} \, dx","Int[(1 + x^(-1/3))/(-1 + x^(-1/3)),x]","-3 x^{2/3}-x-6 \sqrt[3]{x}-6 \log \left(1-\sqrt[3]{x}\right)","-3 x^{2/3}-x-6 \sqrt[3]{x}-6 \log \left(1-\sqrt[3]{x}\right)",1,"-6*x^(1/3) - 3*x^(2/3) - x - 6*Log[1 - x^(1/3)]","A",4,3,17,0.1765,1,"{374, 376, 77}"
281,1,79,0,0.0331956,"\int \left(a-b x^n\right)^{3/2} \left(a+b x^n\right)^{3/2} \, dx","Int[(a - b*x^n)^(3/2)*(a + b*x^n)^(3/2),x]","\frac{a^2 x \sqrt{a-b x^n} \sqrt{a+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{1}{2 n};\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2}\right)}{\sqrt{1-\frac{b^2 x^{2 n}}{a^2}}}","\frac{a^2 x \sqrt{a-b x^n} \sqrt{a+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{1}{2 n};\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2}\right)}{\sqrt{1-\frac{b^2 x^{2 n}}{a^2}}}",1,"(a^2*x*Sqrt[a - b*x^n]*Sqrt[a + b*x^n]*Hypergeometric2F1[-3/2, 1/(2*n), (2 + n^(-1))/2, (b^2*x^(2*n))/a^2])/Sqrt[1 - (b^2*x^(2*n))/a^2]","A",3,3,24,0.1250,1,"{253, 246, 245}"
282,1,76,0,0.0272434,"\int \sqrt{a-b x^n} \sqrt{a+b x^n} \, dx","Int[Sqrt[a - b*x^n]*Sqrt[a + b*x^n],x]","\frac{x \sqrt{a-b x^n} \sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{1}{2 n};\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2}\right)}{\sqrt{1-\frac{b^2 x^{2 n}}{a^2}}}","\frac{x \sqrt{a-b x^n} \sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{1}{2 n};\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2}\right)}{\sqrt{1-\frac{b^2 x^{2 n}}{a^2}}}",1,"(x*Sqrt[a - b*x^n]*Sqrt[a + b*x^n]*Hypergeometric2F1[-1/2, 1/(2*n), (2 + n^(-1))/2, (b^2*x^(2*n))/a^2])/Sqrt[1 - (b^2*x^(2*n))/a^2]","A",3,3,24,0.1250,1,"{253, 246, 245}"
283,1,72,0,0.0285352,"\int \left(a-b x^n\right)^p \left(a+b x^n\right)^p \, dx","Int[(a - b*x^n)^p*(a + b*x^n)^p,x]","x \left(a-b x^n\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(\frac{1}{2 n},-p;\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2}\right)","x \left(a-b x^n\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(\frac{1}{2 n},-p;\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2}\right)",1,"(x*(a - b*x^n)^p*(a + b*x^n)^p*Hypergeometric2F1[1/(2*n), -p, (2 + n^(-1))/2, (b^2*x^(2*n))/a^2])/(1 - (b^2*x^(2*n))/a^2)^p","A",3,3,20,0.1500,1,"{253, 246, 245}"
284,1,132,0,0.111141,"\int \left(a+b x^n\right) \left(c+d x^n\right)^4 \, dx","Int[(a + b*x^n)*(c + d*x^n)^4,x]","\frac{c^3 x^{n+1} (4 a d+b c)}{n+1}+\frac{2 c^2 d x^{2 n+1} (3 a d+2 b c)}{2 n+1}+\frac{2 c d^2 x^{3 n+1} (2 a d+3 b c)}{3 n+1}+\frac{d^3 x^{4 n+1} (a d+4 b c)}{4 n+1}+a c^4 x+\frac{b d^4 x^{5 n+1}}{5 n+1}","\frac{c^3 x^{n+1} (4 a d+b c)}{n+1}+\frac{2 c^2 d x^{2 n+1} (3 a d+2 b c)}{2 n+1}+\frac{2 c d^2 x^{3 n+1} (2 a d+3 b c)}{3 n+1}+\frac{d^3 x^{4 n+1} (a d+4 b c)}{4 n+1}+a c^4 x+\frac{b d^4 x^{5 n+1}}{5 n+1}",1,"a*c^4*x + (c^3*(b*c + 4*a*d)*x^(1 + n))/(1 + n) + (2*c^2*d*(2*b*c + 3*a*d)*x^(1 + 2*n))/(1 + 2*n) + (2*c*d^2*(3*b*c + 2*a*d)*x^(1 + 3*n))/(1 + 3*n) + (d^3*(4*b*c + a*d)*x^(1 + 4*n))/(1 + 4*n) + (b*d^4*x^(1 + 5*n))/(1 + 5*n)","A",2,1,17,0.05882,1,"{373}"
285,1,99,0,0.0727884,"\int \left(a+b x^n\right) \left(c+d x^n\right)^3 \, dx","Int[(a + b*x^n)*(c + d*x^n)^3,x]","\frac{c^2 x^{n+1} (3 a d+b c)}{n+1}+\frac{d^2 x^{3 n+1} (a d+3 b c)}{3 n+1}+\frac{3 c d x^{2 n+1} (a d+b c)}{2 n+1}+a c^3 x+\frac{b d^3 x^{4 n+1}}{4 n+1}","\frac{c^2 x^{n+1} (3 a d+b c)}{n+1}+\frac{d^2 x^{3 n+1} (a d+3 b c)}{3 n+1}+\frac{3 c d x^{2 n+1} (a d+b c)}{2 n+1}+a c^3 x+\frac{b d^3 x^{4 n+1}}{4 n+1}",1,"a*c^3*x + (c^2*(b*c + 3*a*d)*x^(1 + n))/(1 + n) + (3*c*d*(b*c + a*d)*x^(1 + 2*n))/(1 + 2*n) + (d^2*(3*b*c + a*d)*x^(1 + 3*n))/(1 + 3*n) + (b*d^3*x^(1 + 4*n))/(1 + 4*n)","A",2,1,17,0.05882,1,"{373}"
286,1,70,0,0.0451552,"\int \left(a+b x^n\right) \left(c+d x^n\right)^2 \, dx","Int[(a + b*x^n)*(c + d*x^n)^2,x]","\frac{c x^{n+1} (2 a d+b c)}{n+1}+\frac{d x^{2 n+1} (a d+2 b c)}{2 n+1}+a c^2 x+\frac{b d^2 x^{3 n+1}}{3 n+1}","\frac{c x^{n+1} (2 a d+b c)}{n+1}+\frac{d x^{2 n+1} (a d+2 b c)}{2 n+1}+a c^2 x+\frac{b d^2 x^{3 n+1}}{3 n+1}",1,"a*c^2*x + (c*(b*c + 2*a*d)*x^(1 + n))/(1 + n) + (d*(2*b*c + a*d)*x^(1 + 2*n))/(1 + 2*n) + (b*d^2*x^(1 + 3*n))/(1 + 3*n)","A",2,1,17,0.05882,1,"{373}"
287,1,40,0,0.0209865,"\int \left(a+b x^n\right) \left(c+d x^n\right) \, dx","Int[(a + b*x^n)*(c + d*x^n),x]","\frac{x^{n+1} (a d+b c)}{n+1}+a c x+\frac{b d x^{2 n+1}}{2 n+1}","\frac{x^{n+1} (a d+b c)}{n+1}+a c x+\frac{b d x^{2 n+1}}{2 n+1}",1,"a*c*x + ((b*c + a*d)*x^(1 + n))/(1 + n) + (b*d*x^(1 + 2*n))/(1 + 2*n)","A",2,1,15,0.06667,1,"{373}"
288,1,43,0,0.0170337,"\int \frac{a+b x^n}{c+d x^n} \, dx","Int[(a + b*x^n)/(c + d*x^n),x]","\frac{b x}{d}-\frac{x (b c-a d) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c d}","\frac{b x}{d}-\frac{x (b c-a d) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c d}",1,"(b*x)/d - ((b*c - a*d)*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c*d)","A",2,2,17,0.1176,1,"{388, 245}"
289,1,73,0,0.0308483,"\int \frac{a+b x^n}{\left(c+d x^n\right)^2} \, dx","Int[(a + b*x^n)/(c + d*x^n)^2,x]","\frac{x (b c-a d (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c^2 d n}-\frac{x (b c-a d)}{c d n \left(c+d x^n\right)}","\frac{x (b c-a d (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c^2 d n}-\frac{x (b c-a d)}{c d n \left(c+d x^n\right)}",1,"-(((b*c - a*d)*x)/(c*d*n*(c + d*x^n))) + ((b*c - a*d*(1 - n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c^2*d*n)","A",2,2,17,0.1176,1,"{385, 245}"
290,1,78,0,0.0310969,"\int \frac{a+b x^n}{\left(c+d x^n\right)^3} \, dx","Int[(a + b*x^n)/(c + d*x^n)^3,x]","\frac{x (b c-a d (1-2 n)) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{2 c^3 d n}-\frac{x (b c-a d)}{2 c d n \left(c+d x^n\right)^2}","\frac{x (b c-a d (1-2 n)) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{2 c^3 d n}-\frac{x (b c-a d)}{2 c d n \left(c+d x^n\right)^2}",1,"-((b*c - a*d)*x)/(2*c*d*n*(c + d*x^n)^2) + ((b*c - a*d*(1 - 2*n))*x*Hypergeometric2F1[2, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(2*c^3*d*n)","A",2,2,17,0.1176,1,"{385, 245}"
291,1,78,0,0.0307568,"\int \frac{a+b x^n}{\left(c+d x^n\right)^4} \, dx","Int[(a + b*x^n)/(c + d*x^n)^4,x]","\frac{x (b c-a d (1-3 n)) \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{3 c^4 d n}-\frac{x (b c-a d)}{3 c d n \left(c+d x^n\right)^3}","\frac{x (b c-a d (1-3 n)) \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{3 c^4 d n}-\frac{x (b c-a d)}{3 c d n \left(c+d x^n\right)^3}",1,"-((b*c - a*d)*x)/(3*c*d*n*(c + d*x^n)^3) + ((b*c - a*d*(1 - 3*n))*x*Hypergeometric2F1[3, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(3*c^4*d*n)","A",2,2,17,0.1176,1,"{385, 245}"
292,1,158,0,0.1299296,"\int \left(a+b x^n\right)^2 \left(d+e x^n\right)^3 \, dx","Int[(a + b*x^n)^2*(d + e*x^n)^3,x]","\frac{d x^{2 n+1} \left(3 a^2 e^2+6 a b d e+b^2 d^2\right)}{2 n+1}+\frac{e x^{3 n+1} \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)}{3 n+1}+a^2 d^3 x+\frac{a d^2 x^{n+1} (3 a e+2 b d)}{n+1}+\frac{b e^2 x^{4 n+1} (2 a e+3 b d)}{4 n+1}+\frac{b^2 e^3 x^{5 n+1}}{5 n+1}","\frac{d x^{2 n+1} \left(3 a^2 e^2+6 a b d e+b^2 d^2\right)}{2 n+1}+\frac{e x^{3 n+1} \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)}{3 n+1}+a^2 d^3 x+\frac{a d^2 x^{n+1} (3 a e+2 b d)}{n+1}+\frac{b e^2 x^{4 n+1} (2 a e+3 b d)}{4 n+1}+\frac{b^2 e^3 x^{5 n+1}}{5 n+1}",1,"a^2*d^3*x + (a*d^2*(2*b*d + 3*a*e)*x^(1 + n))/(1 + n) + (d*(b^2*d^2 + 6*a*b*d*e + 3*a^2*e^2)*x^(1 + 2*n))/(1 + 2*n) + (e*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2)*x^(1 + 3*n))/(1 + 3*n) + (b*e^2*(3*b*d + 2*a*e)*x^(1 + 4*n))/(1 + 4*n) + (b^2*e^3*x^(1 + 5*n))/(1 + 5*n)","A",2,1,19,0.05263,1,"{373}"
293,1,112,0,0.0816809,"\int \left(a+b x^n\right)^2 \left(d+e x^n\right)^2 \, dx","Int[(a + b*x^n)^2*(d + e*x^n)^2,x]","\frac{x^{2 n+1} \left(a^2 e^2+4 a b d e+b^2 d^2\right)}{2 n+1}+a^2 d^2 x+\frac{2 a d x^{n+1} (a e+b d)}{n+1}+\frac{2 b e x^{3 n+1} (a e+b d)}{3 n+1}+\frac{b^2 e^2 x^{4 n+1}}{4 n+1}","\frac{x^{2 n+1} \left(a^2 e^2+4 a b d e+b^2 d^2\right)}{2 n+1}+a^2 d^2 x+\frac{2 a d x^{n+1} (a e+b d)}{n+1}+\frac{2 b e x^{3 n+1} (a e+b d)}{3 n+1}+\frac{b^2 e^2 x^{4 n+1}}{4 n+1}",1,"a^2*d^2*x + (2*a*d*(b*d + a*e)*x^(1 + n))/(1 + n) + ((b^2*d^2 + 4*a*b*d*e + a^2*e^2)*x^(1 + 2*n))/(1 + 2*n) + (2*b*e*(b*d + a*e)*x^(1 + 3*n))/(1 + 3*n) + (b^2*e^2*x^(1 + 4*n))/(1 + 4*n)","A",2,1,19,0.05263,1,"{373}"
294,1,70,0,0.0471064,"\int \left(a+b x^n\right)^2 \left(c+d x^n\right) \, dx","Int[(a + b*x^n)^2*(c + d*x^n),x]","a^2 c x+\frac{a x^{n+1} (a d+2 b c)}{n+1}+\frac{b x^{2 n+1} (2 a d+b c)}{2 n+1}+\frac{b^2 d x^{3 n+1}}{3 n+1}","a^2 c x+\frac{a x^{n+1} (a d+2 b c)}{n+1}+\frac{b x^{2 n+1} (2 a d+b c)}{2 n+1}+\frac{b^2 d x^{3 n+1}}{3 n+1}",1,"a^2*c*x + (a*(2*b*c + a*d)*x^(1 + n))/(1 + n) + (b*(b*c + 2*a*d)*x^(1 + 2*n))/(1 + 2*n) + (b^2*d*x^(1 + 3*n))/(1 + 3*n)","A",2,1,17,0.05882,1,"{373}"
295,1,84,0,0.0940034,"\int \frac{\left(a+b x^n\right)^2}{c+d x^n} \, dx","Int[(a + b*x^n)^2/(c + d*x^n),x]","\frac{x (b c-a d)^2 \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c d^2}-\frac{b x (b c (n+1)-a d (2 n+1))}{d^2 (n+1)}+\frac{b x \left(a+b x^n\right)}{d (n+1)}","\frac{x (b c-a d)^2 \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c d^2}-\frac{b x (b c (n+1)-a d (2 n+1))}{d^2 (n+1)}+\frac{b x \left(a+b x^n\right)}{d (n+1)}",1,"-((b*(b*c*(1 + n) - a*d*(1 + 2*n))*x)/(d^2*(1 + n))) + (b*x*(a + b*x^n))/(d*(1 + n)) + ((b*c - a*d)^2*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c*d^2)","A",3,3,19,0.1579,1,"{416, 388, 245}"
296,1,115,0,0.092344,"\int \frac{\left(a+b x^n\right)^2}{\left(c+d x^n\right)^2} \, dx","Int[(a + b*x^n)^2/(c + d*x^n)^2,x]","\frac{x (b c-a d) (a d (1-n)-b c (n+1)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c^2 d^2 n}-\frac{b x (a d-b c (n+1))}{c d^2 n}-\frac{x (b c-a d) \left(a+b x^n\right)}{c d n \left(c+d x^n\right)}","\frac{x (b c-a d) (a d (1-n)-b c (n+1)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c^2 d^2 n}-\frac{b x (a d-b c (n+1))}{c d^2 n}-\frac{x (b c-a d) \left(a+b x^n\right)}{c d n \left(c+d x^n\right)}",1,"-((b*(a*d - b*c*(1 + n))*x)/(c*d^2*n)) - ((b*c - a*d)*x*(a + b*x^n))/(c*d*n*(c + d*x^n)) + ((b*c - a*d)*(a*d*(1 - n) - b*c*(1 + n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c^2*d^2*n)","A",3,3,19,0.1579,1,"{413, 388, 245}"
297,1,160,0,0.1596026,"\int \frac{\left(a+b x^n\right)^2}{\left(c+d x^n\right)^3} \, dx","Int[(a + b*x^n)^2/(c + d*x^n)^3,x]","-\frac{x \left(-a^2 d^2 \left(2 n^2-3 n+1\right)+2 a b c d (1-n)-b^2 c^2 (n+1)\right) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{2 c^3 d^2 n^2}+\frac{x (b c-a d) (a d (1-2 n)-b c (n+1))}{2 c^2 d^2 n^2 \left(c+d x^n\right)}-\frac{x (b c-a d) \left(a+b x^n\right)}{2 c d n \left(c+d x^n\right)^2}","-\frac{x \left(-a^2 d^2 \left(2 n^2-3 n+1\right)+2 a b c d (1-n)-b^2 c^2 (n+1)\right) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{2 c^3 d^2 n^2}+\frac{x (b c-a d) (a d (1-2 n)-b c (n+1))}{2 c^2 d^2 n^2 \left(c+d x^n\right)}-\frac{x (b c-a d) \left(a+b x^n\right)}{2 c d n \left(c+d x^n\right)^2}",1,"-((b*c - a*d)*x*(a + b*x^n))/(2*c*d*n*(c + d*x^n)^2) + ((b*c - a*d)*(a*d*(1 - 2*n) - b*c*(1 + n))*x)/(2*c^2*d^2*n^2*(c + d*x^n)) - ((2*a*b*c*d*(1 - n) - b^2*c^2*(1 + n) - a^2*d^2*(1 - 3*n + 2*n^2))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(2*c^3*d^2*n^2)","A",3,3,19,0.1579,1,"{413, 385, 245}"
298,1,310,0,0.5010125,"\int \frac{\left(c+d x^n\right)^4}{a+b x^n} \, dx","Int[(c + d*x^n)^4/(a + b*x^n),x]","-\frac{d x \left(c+d x^n\right) \left(-a^2 d^2 \left(6 n^2+5 n+1\right)+2 a b c d (3 n+1)^2-b^2 c^2 \left(18 n^2+7 n+1\right)\right)}{b^3 (n+1) (2 n+1) (3 n+1)}-\frac{d x \left(-a^2 b c d^2 \left(24 n^3+38 n^2+19 n+3\right)+a^3 d^3 \left(6 n^3+11 n^2+6 n+1\right)+a b^2 c^2 d \left(36 n^3+45 n^2+20 n+3\right)-b^3 c^3 \left(24 n^3+18 n^2+7 n+1\right)\right)}{b^4 (n+1) (2 n+1) (3 n+1)}+\frac{x (b c-a d)^4 \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a b^4}-\frac{d x \left(c+d x^n\right)^2 (a d (3 n+1)-b (6 c n+c))}{b^2 \left(6 n^2+5 n+1\right)}+\frac{d x \left(c+d x^n\right)^3}{b (3 n+1)}","-\frac{d x \left(c+d x^n\right) \left(-a^2 d^2 \left(6 n^2+5 n+1\right)+2 a b c d (3 n+1)^2-b^2 c^2 \left(18 n^2+7 n+1\right)\right)}{b^3 (n+1) (2 n+1) (3 n+1)}-\frac{d x \left(-a^2 b c d^2 \left(24 n^3+38 n^2+19 n+3\right)+a^3 d^3 \left(6 n^3+11 n^2+6 n+1\right)+a b^2 c^2 d \left(36 n^3+45 n^2+20 n+3\right)-b^3 c^3 \left(24 n^3+18 n^2+7 n+1\right)\right)}{b^4 (n+1) (2 n+1) (3 n+1)}+\frac{x (b c-a d)^4 \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a b^4}-\frac{d x \left(c+d x^n\right)^2 (a d (3 n+1)-b (6 c n+c))}{b^2 \left(6 n^2+5 n+1\right)}+\frac{d x \left(c+d x^n\right)^3}{b (3 n+1)}",1,"-((d*(a^3*d^3*(1 + 6*n + 11*n^2 + 6*n^3) - b^3*c^3*(1 + 7*n + 18*n^2 + 24*n^3) - a^2*b*c*d^2*(3 + 19*n + 38*n^2 + 24*n^3) + a*b^2*c^2*d*(3 + 20*n + 45*n^2 + 36*n^3))*x)/(b^4*(1 + n)*(1 + 2*n)*(1 + 3*n))) - (d*(2*a*b*c*d*(1 + 3*n)^2 - a^2*d^2*(1 + 5*n + 6*n^2) - b^2*c^2*(1 + 7*n + 18*n^2))*x*(c + d*x^n))/(b^3*(1 + n)*(1 + 2*n)*(1 + 3*n)) - (d*(a*d*(1 + 3*n) - b*(c + 6*c*n))*x*(c + d*x^n)^2)/(b^2*(1 + 5*n + 6*n^2)) + (d*x*(c + d*x^n)^3)/(b*(1 + 3*n)) + ((b*c - a*d)^4*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*b^4)","A",5,4,19,0.2105,1,"{416, 528, 388, 245}"
299,1,173,0,0.2672492,"\int \frac{\left(c+d x^n\right)^3}{a+b x^n} \, dx","Int[(c + d*x^n)^3/(a + b*x^n),x]","\frac{d x \left(a^2 d^2 \left(2 n^2+3 n+1\right)-a b c d \left(6 n^2+7 n+2\right)+b^2 c^2 \left(6 n^2+4 n+1\right)\right)}{b^3 (n+1) (2 n+1)}+\frac{x (b c-a d)^3 \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a b^3}-\frac{d x \left(c+d x^n\right) (a d (2 n+1)-b (4 c n+c))}{b^2 (n+1) (2 n+1)}+\frac{d x \left(c+d x^n\right)^2}{b (2 n+1)}","\frac{d x \left(a^2 d^2 \left(2 n^2+3 n+1\right)-a b c d \left(6 n^2+7 n+2\right)+b^2 c^2 \left(6 n^2+4 n+1\right)\right)}{b^3 (n+1) (2 n+1)}+\frac{x (b c-a d)^3 \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a b^3}-\frac{d x \left(c+d x^n\right) (a d (2 n+1)-b (4 c n+c))}{b^2 (n+1) (2 n+1)}+\frac{d x \left(c+d x^n\right)^2}{b (2 n+1)}",1,"(d*(a^2*d^2*(1 + 3*n + 2*n^2) + b^2*c^2*(1 + 4*n + 6*n^2) - a*b*c*d*(2 + 7*n + 6*n^2))*x)/(b^3*(1 + n)*(1 + 2*n)) - (d*(a*d*(1 + 2*n) - b*(c + 4*c*n))*x*(c + d*x^n))/(b^2*(1 + n)*(1 + 2*n)) + (d*x*(c + d*x^n)^2)/(b*(1 + 2*n)) + ((b*c - a*d)^3*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*b^3)","A",4,4,19,0.2105,1,"{416, 528, 388, 245}"
300,1,84,0,0.0974269,"\int \frac{\left(c+d x^n\right)^2}{a+b x^n} \, dx","Int[(c + d*x^n)^2/(a + b*x^n),x]","\frac{x (b c-a d)^2 \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a b^2}-\frac{d x (a d (n+1)-b (2 c n+c))}{b^2 (n+1)}+\frac{d x \left(c+d x^n\right)}{b (n+1)}","\frac{x (b c-a d)^2 \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a b^2}-\frac{d x (a d (n+1)-b (2 c n+c))}{b^2 (n+1)}+\frac{d x \left(c+d x^n\right)}{b (n+1)}",1,"-((d*(a*d*(1 + n) - b*(c + 2*c*n))*x)/(b^2*(1 + n))) + (d*x*(c + d*x^n))/(b*(1 + n)) + ((b*c - a*d)^2*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*b^2)","A",3,3,19,0.1579,1,"{416, 388, 245}"
301,1,42,0,0.0159626,"\int \frac{c+d x^n}{a+b x^n} \, dx","Int[(c + d*x^n)/(a + b*x^n),x]","\frac{x (b c-a d) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a b}+\frac{d x}{b}","\frac{x (b c-a d) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a b}+\frac{d x}{b}",1,"(d*x)/b + ((b*c - a*d)*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*b)","A",2,2,17,0.1176,1,"{388, 245}"
302,1,72,0,0.0258087,"\int \frac{1}{\left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[1/((a + b*x^n)*(c + d*x^n)),x]","\frac{b x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (b c-a d)}-\frac{d x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c (b c-a d)}","\frac{b x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (b c-a d)}-\frac{d x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c (b c-a d)}",1,"(b*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*(b*c - a*d)) - (d*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c*(b*c - a*d))","A",3,2,19,0.1053,1,"{391, 245}"
303,1,123,0,0.1459599,"\int \frac{1}{\left(a+b x^n\right) \left(c+d x^n\right)^2} \, dx","Int[1/((a + b*x^n)*(c + d*x^n)^2),x]","\frac{b^2 x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (b c-a d)^2}+\frac{d x (b c (1-2 n)-a d (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c^2 n (b c-a d)^2}-\frac{d x}{c n (b c-a d) \left(c+d x^n\right)}","\frac{b^2 x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (b c-a d)^2}+\frac{d x (b c (1-2 n)-a d (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c^2 n (b c-a d)^2}-\frac{d x}{c n (b c-a d) \left(c+d x^n\right)}",1,"-((d*x)/(c*(b*c - a*d)*n*(c + d*x^n))) + (b^2*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*(b*c - a*d)^2) + (d*(b*c*(1 - 2*n) - a*d*(1 - n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c^2*(b*c - a*d)^2*n)","A",4,3,19,0.1579,1,"{414, 522, 245}"
304,1,210,0,0.3286711,"\int \frac{1}{\left(a+b x^n\right) \left(c+d x^n\right)^3} \, dx","Int[1/((a + b*x^n)*(c + d*x^n)^3),x]","-\frac{d x \left(a^2 d^2 \left(2 n^2-3 n+1\right)-2 a b c d \left(3 n^2-4 n+1\right)+b^2 c^2 \left(6 n^2-5 n+1\right)\right) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{2 c^3 n^2 (b c-a d)^3}+\frac{b^3 x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (b c-a d)^3}-\frac{d x (a d (1-2 n)-b (c-4 c n))}{2 c^2 n^2 (b c-a d)^2 \left(c+d x^n\right)}-\frac{d x}{2 c n (b c-a d) \left(c+d x^n\right)^2}","-\frac{d x \left(a^2 d^2 \left(2 n^2-3 n+1\right)-2 a b c d \left(3 n^2-4 n+1\right)+b^2 c^2 \left(6 n^2-5 n+1\right)\right) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{2 c^3 n^2 (b c-a d)^3}+\frac{b^3 x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (b c-a d)^3}-\frac{d x (a d (1-2 n)-b (c-4 c n))}{2 c^2 n^2 (b c-a d)^2 \left(c+d x^n\right)}-\frac{d x}{2 c n (b c-a d) \left(c+d x^n\right)^2}",1,"-(d*x)/(2*c*(b*c - a*d)*n*(c + d*x^n)^2) - (d*(a*d*(1 - 2*n) - b*(c - 4*c*n))*x)/(2*c^2*(b*c - a*d)^2*n^2*(c + d*x^n)) + (b^3*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*(b*c - a*d)^3) - (d*(a^2*d^2*(1 - 3*n + 2*n^2) - 2*a*b*c*d*(1 - 4*n + 3*n^2) + b^2*c^2*(1 - 5*n + 6*n^2))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(2*c^3*(b*c - a*d)^3*n^2)","A",5,4,19,0.2105,1,"{414, 527, 522, 245}"
305,1,341,0,0.5479046,"\int \frac{\left(c+d x^n\right)^4}{\left(a+b x^n\right)^2} \, dx","Int[(c + d*x^n)^4/(a + b*x^n)^2,x]","-\frac{d x \left(c+d x^n\right) \left(a^2 d^2 \left(6 n^2+5 n+1\right)-2 a b c d \left(5 n^2+4 n+1\right)+b^2 c^2 \left(2 n^2+3 n+1\right)\right)}{a b^3 n (n+1) (2 n+1)}-\frac{d x \left(a^2 b c d^2 \left(16 n^3+26 n^2+15 n+3\right)-a^3 d^3 \left(6 n^3+11 n^2+6 n+1\right)-a b^2 c^2 d \left(12 n^3+17 n^2+12 n+3\right)+b^3 c^3 \left(2 n^2+3 n+1\right)\right)}{a b^4 n (n+1) (2 n+1)}-\frac{x (b c-a d)^3 (b c (1-n)-a d (3 n+1)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b^4 n}+\frac{d x \left(c+d x^n\right)^2 (a d (3 n+1)-b (2 c n+c))}{a b^2 n (2 n+1)}+\frac{x (b c-a d) \left(c+d x^n\right)^3}{a b n \left(a+b x^n\right)}","-\frac{d x \left(c+d x^n\right) \left(a^2 d^2 \left(6 n^2+5 n+1\right)-2 a b c d \left(5 n^2+4 n+1\right)+b^2 c^2 \left(2 n^2+3 n+1\right)\right)}{a b^3 n (n+1) (2 n+1)}-\frac{d x \left(a^2 b c d^2 \left(16 n^3+26 n^2+15 n+3\right)-a^3 d^3 \left(6 n^3+11 n^2+6 n+1\right)-a b^2 c^2 d \left(12 n^3+17 n^2+12 n+3\right)+b^3 c^3 \left(2 n^2+3 n+1\right)\right)}{a b^4 n (n+1) (2 n+1)}-\frac{x (b c-a d)^3 (b c (1-n)-a d (3 n+1)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b^4 n}+\frac{d x \left(c+d x^n\right)^2 (a d (3 n+1)-b (2 c n+c))}{a b^2 n (2 n+1)}+\frac{x (b c-a d) \left(c+d x^n\right)^3}{a b n \left(a+b x^n\right)}",1,"-((d*(b^3*c^3*(1 + 3*n + 2*n^2) - a^3*d^3*(1 + 6*n + 11*n^2 + 6*n^3) - a*b^2*c^2*d*(3 + 12*n + 17*n^2 + 12*n^3) + a^2*b*c*d^2*(3 + 15*n + 26*n^2 + 16*n^3))*x)/(a*b^4*n*(1 + n)*(1 + 2*n))) - (d*(b^2*c^2*(1 + 3*n + 2*n^2) - 2*a*b*c*d*(1 + 4*n + 5*n^2) + a^2*d^2*(1 + 5*n + 6*n^2))*x*(c + d*x^n))/(a*b^3*n*(1 + n)*(1 + 2*n)) + (d*(a*d*(1 + 3*n) - b*(c + 2*c*n))*x*(c + d*x^n)^2)/(a*b^2*n*(1 + 2*n)) + ((b*c - a*d)*x*(c + d*x^n)^3)/(a*b*n*(a + b*x^n)) - ((b*c - a*d)^3*(b*c*(1 - n) - a*d*(1 + 3*n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*b^4*n)","A",5,4,19,0.2105,1,"{413, 528, 388, 245}"
306,1,200,0,0.2596784,"\int \frac{\left(c+d x^n\right)^3}{\left(a+b x^n\right)^2} \, dx","Int[(c + d*x^n)^3/(a + b*x^n)^2,x]","-\frac{d x \left(a^2 d^2 \left(2 n^2+3 n+1\right)-a b c d \left(3 n^2+4 n+2\right)+b^2 c^2 (n+1)\right)}{a b^3 n (n+1)}-\frac{x (b c-a d)^2 (b c (1-n)-a d (2 n+1)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b^3 n}-\frac{d x \left(c+d x^n\right) (b c (n+1)-a d (2 n+1))}{a b^2 n (n+1)}+\frac{x (b c-a d) \left(c+d x^n\right)^2}{a b n \left(a+b x^n\right)}","-\frac{d x \left(a^2 d^2 \left(2 n^2+3 n+1\right)-a b c d \left(3 n^2+4 n+2\right)+b^2 c^2 (n+1)\right)}{a b^3 n (n+1)}-\frac{x (b c-a d)^2 (b c (1-n)-a d (2 n+1)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b^3 n}-\frac{d x \left(c+d x^n\right) (b c (n+1)-a d (2 n+1))}{a b^2 n (n+1)}+\frac{x (b c-a d) \left(c+d x^n\right)^2}{a b n \left(a+b x^n\right)}",1,"-((d*(b^2*c^2*(1 + n) + a^2*d^2*(1 + 3*n + 2*n^2) - a*b*c*d*(2 + 4*n + 3*n^2))*x)/(a*b^3*n*(1 + n))) - (d*(b*c*(1 + n) - a*d*(1 + 2*n))*x*(c + d*x^n))/(a*b^2*n*(1 + n)) + ((b*c - a*d)*x*(c + d*x^n)^2)/(a*b*n*(a + b*x^n)) - ((b*c - a*d)^2*(b*c*(1 - n) - a*d*(1 + 2*n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*b^3*n)","A",4,4,19,0.2105,1,"{413, 528, 388, 245}"
307,1,115,0,0.0939848,"\int \frac{\left(c+d x^n\right)^2}{\left(a+b x^n\right)^2} \, dx","Int[(c + d*x^n)^2/(a + b*x^n)^2,x]","-\frac{x (b c-a d) (b c (1-n)-a d (n+1)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b^2 n}-\frac{d x (b c-a d (n+1))}{a b^2 n}+\frac{x (b c-a d) \left(c+d x^n\right)}{a b n \left(a+b x^n\right)}","-\frac{x (b c-a d) (b c (1-n)-a d (n+1)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b^2 n}-\frac{d x (b c-a d (n+1))}{a b^2 n}+\frac{x (b c-a d) \left(c+d x^n\right)}{a b n \left(a+b x^n\right)}",1,"-((d*(b*c - a*d*(1 + n))*x)/(a*b^2*n)) + ((b*c - a*d)*x*(c + d*x^n))/(a*b*n*(a + b*x^n)) - ((b*c - a*d)*(b*c*(1 - n) - a*d*(1 + n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*b^2*n)","A",3,3,19,0.1579,1,"{413, 388, 245}"
308,1,72,0,0.0307196,"\int \frac{c+d x^n}{\left(a+b x^n\right)^2} \, dx","Int[(c + d*x^n)/(a + b*x^n)^2,x]","\frac{x (a d-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b n}+\frac{x (b c-a d)}{a b n \left(a+b x^n\right)}","\frac{x (a d-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b n}+\frac{x (b c-a d)}{a b n \left(a+b x^n\right)}",1,"((b*c - a*d)*x)/(a*b*n*(a + b*x^n)) + ((a*d - b*c*(1 - n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*b*n)","A",2,2,17,0.1176,1,"{385, 245}"
309,1,122,0,0.1422946,"\int \frac{1}{\left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[1/((a + b*x^n)^2*(c + d*x^n)),x]","\frac{b x (a d (1-2 n)-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 n (b c-a d)^2}+\frac{d^2 x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c (b c-a d)^2}+\frac{b x}{a n (b c-a d) \left(a+b x^n\right)}","\frac{b x (a d (1-2 n)-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 n (b c-a d)^2}+\frac{d^2 x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c (b c-a d)^2}+\frac{b x}{a n (b c-a d) \left(a+b x^n\right)}",1,"(b*x)/(a*(b*c - a*d)*n*(a + b*x^n)) + (b*(a*d*(1 - 2*n) - b*c*(1 - n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*(b*c - a*d)^2*n) + (d^2*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c*(b*c - a*d)^2)","A",4,3,19,0.1579,1,"{414, 522, 245}"
310,1,193,0,0.2710055,"\int \frac{1}{\left(a+b x^n\right)^2 \left(c+d x^n\right)^2} \, dx","Int[1/((a + b*x^n)^2*(c + d*x^n)^2),x]","\frac{b^2 x (a d (1-3 n)-b (c-c n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 n (b c-a d)^3}-\frac{d^2 x (b c (1-3 n)-a d (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c^2 n (b c-a d)^3}+\frac{b x}{a n (b c-a d) \left(a+b x^n\right) \left(c+d x^n\right)}+\frac{d x (a d+b c)}{a c n (b c-a d)^2 \left(c+d x^n\right)}","\frac{b^2 x (a d (1-3 n)-b (c-c n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 n (b c-a d)^3}-\frac{d^2 x (b c (1-3 n)-a d (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c^2 n (b c-a d)^3}+\frac{b x}{a n (b c-a d) \left(a+b x^n\right) \left(c+d x^n\right)}+\frac{d x (a d+b c)}{a c n (b c-a d)^2 \left(c+d x^n\right)}",1,"(d*(b*c + a*d)*x)/(a*c*(b*c - a*d)^2*n*(c + d*x^n)) + (b*x)/(a*(b*c - a*d)*n*(a + b*x^n)*(c + d*x^n)) + (b^2*(a*d*(1 - 3*n) - b*(c - c*n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*(b*c - a*d)^3*n) - (d^2*(b*c*(1 - 3*n) - a*d*(1 - n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c^2*(b*c - a*d)^3*n)","A",5,4,19,0.2105,1,"{414, 527, 522, 245}"
311,1,299,0,0.5468926,"\int \frac{1}{\left(a+b x^n\right)^2 \left(c+d x^n\right)^3} \, dx","Int[1/((a + b*x^n)^2*(c + d*x^n)^3),x]","\frac{d^2 x \left(a^2 d^2 \left(2 n^2-3 n+1\right)-2 a b c d \left(4 n^2-5 n+1\right)+b^2 c^2 \left(12 n^2-7 n+1\right)\right) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{2 c^3 n^2 (b c-a d)^4}-\frac{d x \left(-a^2 d^2 (1-2 n)+a b c d (1-6 n)-2 b^2 c^2 n\right)}{2 a c^2 n^2 (b c-a d)^3 \left(c+d x^n\right)}+\frac{b^3 x (a d (1-4 n)-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 n (b c-a d)^4}+\frac{b x}{a n (b c-a d) \left(a+b x^n\right) \left(c+d x^n\right)^2}+\frac{d x (a d+2 b c)}{2 a c n (b c-a d)^2 \left(c+d x^n\right)^2}","\frac{d^2 x \left(a^2 d^2 \left(2 n^2-3 n+1\right)-2 a b c d \left(4 n^2-5 n+1\right)+b^2 c^2 \left(12 n^2-7 n+1\right)\right) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{2 c^3 n^2 (b c-a d)^4}-\frac{d x \left(-a^2 d^2 (1-2 n)+a b c d (1-6 n)-2 b^2 c^2 n\right)}{2 a c^2 n^2 (b c-a d)^3 \left(c+d x^n\right)}+\frac{b^3 x (a d (1-4 n)-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 n (b c-a d)^4}+\frac{b x}{a n (b c-a d) \left(a+b x^n\right) \left(c+d x^n\right)^2}+\frac{d x (a d+2 b c)}{2 a c n (b c-a d)^2 \left(c+d x^n\right)^2}",1,"(d*(2*b*c + a*d)*x)/(2*a*c*(b*c - a*d)^2*n*(c + d*x^n)^2) + (b*x)/(a*(b*c - a*d)*n*(a + b*x^n)*(c + d*x^n)^2) - (d*(a*b*c*d*(1 - 6*n) - a^2*d^2*(1 - 2*n) - 2*b^2*c^2*n)*x)/(2*a*c^2*(b*c - a*d)^3*n^2*(c + d*x^n)) + (b^3*(a*d*(1 - 4*n) - b*c*(1 - n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*(b*c - a*d)^4*n) + (d^2*(a^2*d^2*(1 - 3*n + 2*n^2) - 2*a*b*c*d*(1 - 5*n + 4*n^2) + b^2*c^2*(1 - 7*n + 12*n^2))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(2*c^3*(b*c - a*d)^4*n^2)","A",6,4,19,0.2105,1,"{414, 527, 522, 245}"
312,1,81,0,0.052638,"\int \left(a+b x^n\right)^p \left(c+d x^n\right)^q \, dx","Int[(a + b*x^n)^p*(c + d*x^n)^q,x]","x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} F_1\left(\frac{1}{n};-p,-q;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)","x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} F_1\left(\frac{1}{n};-p,-q;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)",1,"(x*(a + b*x^n)^p*(c + d*x^n)^q*AppellF1[n^(-1), -p, -q, 1 + n^(-1), -((b*x^n)/a), -((d*x^n)/c)])/((1 + (b*x^n)/a)^p*(1 + (d*x^n)/c)^q)","A",3,2,19,0.1053,1,"{430, 429}"
313,1,401,0,0.5781848,"\int \left(a+b x^n\right)^p \left(c+d x^n\right)^3 \, dx","Int[(a + b*x^n)^p*(c + d*x^n)^3,x]","-\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(-3 a^2 b c d^2 (n+1) (n (p+3)+1)+a^3 d^3 \left(2 n^2+3 n+1\right)+3 a b^2 c^2 d \left(n^2 \left(p^2+5 p+6\right)+n (2 p+5)+1\right)-b^3 c^3 \left(n^3 \left(p^3+6 p^2+11 p+6\right)+n^2 \left(3 p^2+12 p+11\right)+3 n (p+2)+1\right)\right) \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)}{b^3 (n p+n+1) (n (p+2)+1) (n (p+3)+1)}+\frac{d x \left(a+b x^n\right)^{p+1} \left(a^2 d^2 \left(2 n^2+3 n+1\right)-a b c d \left(n^2 (p+7)+n (2 p+9)+2\right)+b^2 c^2 \left(n^2 \left(p^2+6 p+11\right)+2 n (p+3)+1\right)\right)}{b^3 (n p+n+1) (n (p+2)+1) (n (p+3)+1)}-\frac{d x \left(c+d x^n\right) \left(a+b x^n\right)^{p+1} (a d (2 n+1)-b (c n (p+5)+c))}{b^2 (n (p+2)+1) (n (p+3)+1)}+\frac{d x \left(c+d x^n\right)^2 \left(a+b x^n\right)^{p+1}}{b (n (p+3)+1)}","-\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(-3 a^2 b c d^2 (n+1) (n (p+3)+1)+a^3 d^3 \left(2 n^2+3 n+1\right)+3 a b^2 c^2 d \left(n^2 \left(p^2+5 p+6\right)+n (2 p+5)+1\right)-b^3 c^3 \left(n^3 \left(p^3+6 p^2+11 p+6\right)+n^2 \left(3 p^2+12 p+11\right)+3 n (p+2)+1\right)\right) \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)}{b^3 (n p+n+1) (n (p+2)+1) (n (p+3)+1)}+\frac{d x \left(a+b x^n\right)^{p+1} \left(a^2 d^2 \left(2 n^2+3 n+1\right)-a b c d \left(n^2 (p+7)+n (2 p+9)+2\right)+b^2 c^2 \left(n^2 \left(p^2+6 p+11\right)+2 n (p+3)+1\right)\right)}{b^3 (n p+n+1) (n (p+2)+1) (n (p+3)+1)}-\frac{d x \left(c+d x^n\right) \left(a+b x^n\right)^{p+1} (a d (2 n+1)-b c (n (p+5)+1))}{b^2 (n (p+2)+1) (n (p+3)+1)}+\frac{d x \left(c+d x^n\right)^2 \left(a+b x^n\right)^{p+1}}{b (n p+3 n+1)}",1,"(d*(a^2*d^2*(1 + 3*n + 2*n^2) - a*b*c*d*(2 + n^2*(7 + p) + n*(9 + 2*p)) + b^2*c^2*(1 + 2*n*(3 + p) + n^2*(11 + 6*p + p^2)))*x*(a + b*x^n)^(1 + p))/(b^3*(1 + n + n*p)*(1 + n*(2 + p))*(1 + n*(3 + p))) - (d*(a*d*(1 + 2*n) - b*(c + c*n*(5 + p)))*x*(a + b*x^n)^(1 + p)*(c + d*x^n))/(b^2*(1 + n*(2 + p))*(1 + n*(3 + p))) + (d*x*(a + b*x^n)^(1 + p)*(c + d*x^n)^2)/(b*(1 + n*(3 + p))) - ((a^3*d^3*(1 + 3*n + 2*n^2) - 3*a^2*b*c*d^2*(1 + n)*(1 + n*(3 + p)) + 3*a*b^2*c^2*d*(1 + n*(5 + 2*p) + n^2*(6 + 5*p + p^2)) - b^3*c^3*(1 + 3*n*(2 + p) + n^2*(11 + 12*p + 3*p^2) + n^3*(6 + 11*p + 6*p^2 + p^3)))*x*(a + b*x^n)^p*Hypergeometric2F1[n^(-1), -p, 1 + n^(-1), -((b*x^n)/a)])/(b^3*(1 + n + n*p)*(1 + n*(2 + p))*(1 + n*(3 + p))*(1 + (b*x^n)/a)^p)","A",5,5,19,0.2632,1,"{416, 528, 388, 246, 245}"
314,1,197,0,0.26866,"\int \left(a+b x^n\right)^p \left(c+d x^n\right)^2 \, dx","Int[(a + b*x^n)^p*(c + d*x^n)^2,x]","-\frac{d x \left(a+b x^n\right)^{p+1} (a d (n+1)-b (c n (p+3)+c))}{b^2 (n p+n+1) (n (p+2)+1)}-\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(c (a d-b (c n (p+2)+c))-\frac{a d (a d (n+1)-b (c n (p+3)+c))}{b (n p+n+1)}\right) \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)}{b (n (p+2)+1)}+\frac{d x \left(c+d x^n\right) \left(a+b x^n\right)^{p+1}}{b (n (p+2)+1)}","-\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} (b c (n p+n+1) (a d-b c (n (p+2)+1))-a d (a d (n+1)-b c (n (p+3)+1))) \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)}{b^2 (n p+n+1) (n (p+2)+1)}-\frac{d x \left(a+b x^n\right)^{p+1} (a d (n+1)-b c (n (p+3)+1))}{b^2 (n p+n+1) (n (p+2)+1)}+\frac{d x \left(c+d x^n\right) \left(a+b x^n\right)^{p+1}}{b (n p+2 n+1)}",1,"-((d*(a*d*(1 + n) - b*(c + c*n*(3 + p)))*x*(a + b*x^n)^(1 + p))/(b^2*(1 + n + n*p)*(1 + n*(2 + p)))) + (d*x*(a + b*x^n)^(1 + p)*(c + d*x^n))/(b*(1 + n*(2 + p))) - ((c*(a*d - b*(c + c*n*(2 + p))) - (a*d*(a*d*(1 + n) - b*(c + c*n*(3 + p))))/(b*(1 + n + n*p)))*x*(a + b*x^n)^p*Hypergeometric2F1[n^(-1), -p, 1 + n^(-1), -((b*x^n)/a)])/(b*(1 + n*(2 + p))*(1 + (b*x^n)/a)^p)","A",4,4,19,0.2105,1,"{416, 388, 246, 245}"
315,1,89,0,0.0473692,"\int \left(a+b x^n\right)^p \left(c+d x^n\right) \, dx","Int[(a + b*x^n)^p*(c + d*x^n),x]","x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(c-\frac{a d}{b n p+b n+b}\right) \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)+\frac{d x \left(a+b x^n\right)^{p+1}}{b (n p+n+1)}","\frac{d x \left(a+b x^n\right)^{p+1}}{b (n p+n+1)}-\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} (a d-b c (n p+n+1)) \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)}{b (n p+n+1)}",1,"(d*x*(a + b*x^n)^(1 + p))/(b*(1 + n + n*p)) + ((c - (a*d)/(b + b*n + b*n*p))*x*(a + b*x^n)^p*Hypergeometric2F1[n^(-1), -p, 1 + n^(-1), -((b*x^n)/a)])/(1 + (b*x^n)/a)^p","A",3,3,17,0.1765,1,"{388, 246, 245}"
316,1,46,0,0.0108094,"\int \left(a+b x^n\right)^p \, dx","Int[(a + b*x^n)^p,x]","x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)","x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)",1,"(x*(a + b*x^n)^p*Hypergeometric2F1[n^(-1), -p, 1 + n^(-1), -((b*x^n)/a)])/(1 + (b*x^n)/a)^p","A",2,2,9,0.2222,1,"{246, 245}"
317,1,59,0,0.0289819,"\int \frac{\left(a+b x^n\right)^p}{c+d x^n} \, dx","Int[(a + b*x^n)^p/(c + d*x^n),x]","\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} F_1\left(\frac{1}{n};-p,1;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c}","\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} F_1\left(\frac{1}{n};-p,1;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c}",1,"(x*(a + b*x^n)^p*AppellF1[n^(-1), -p, 1, 1 + n^(-1), -((b*x^n)/a), -((d*x^n)/c)])/(c*(1 + (b*x^n)/a)^p)","A",2,2,19,0.1053,1,"{430, 429}"
318,1,59,0,0.0295756,"\int \frac{\left(a+b x^n\right)^p}{\left(c+d x^n\right)^2} \, dx","Int[(a + b*x^n)^p/(c + d*x^n)^2,x]","\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} F_1\left(\frac{1}{n};-p,2;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c^2}","\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} F_1\left(\frac{1}{n};-p,2;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c^2}",1,"(x*(a + b*x^n)^p*AppellF1[n^(-1), -p, 2, 1 + n^(-1), -((b*x^n)/a), -((d*x^n)/c)])/(c^2*(1 + (b*x^n)/a)^p)","A",2,2,19,0.1053,1,"{430, 429}"
319,1,59,0,0.0287971,"\int \frac{\left(a+b x^n\right)^p}{\left(c+d x^n\right)^3} \, dx","Int[(a + b*x^n)^p/(c + d*x^n)^3,x]","\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} F_1\left(\frac{1}{n};-p,3;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c^3}","\frac{x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} F_1\left(\frac{1}{n};-p,3;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c^3}",1,"(x*(a + b*x^n)^p*AppellF1[n^(-1), -p, 3, 1 + n^(-1), -((b*x^n)/a), -((d*x^n)/c)])/(c^3*(1 + (b*x^n)/a)^p)","A",2,2,19,0.1053,1,"{430, 429}"
320,1,93,0,0.0219041,"\int \left(a+b x^n\right)^p \left(c+d x^n\right)^{-1-\frac{1}{n}-p} \, dx","Int[(a + b*x^n)^p*(c + d*x^n)^(-1 - n^(-1) - p),x]","\frac{x \left(a+b x^n\right)^p \left(c+d x^n\right)^{-\frac{1}{n}-p} \left(\frac{c \left(a+b x^n\right)}{a \left(c+d x^n\right)}\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{c}","\frac{x \left(a+b x^n\right)^p \left(c+d x^n\right)^{-\frac{1}{n}-p} \left(\frac{c \left(a+b x^n\right)}{a \left(c+d x^n\right)}\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{c}",1,"(x*(a + b*x^n)^p*(c + d*x^n)^(-n^(-1) - p)*Hypergeometric2F1[n^(-1), -p, 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/(c*((c*(a + b*x^n))/(a*(c + d*x^n)))^p)","A",1,1,28,0.03571,1,"{380}"
321,1,178,0,0.0859997,"\int \left(a+b x^n\right)^3 \left(c+d x^n\right)^{-4-\frac{1}{n}} \, dx","Int[(a + b*x^n)^3*(c + d*x^n)^(-4 - n^(-1)),x]","\frac{6 a^2 n^2 x \left(a+b x^n\right) \left(c+d x^n\right)^{-\frac{1}{n}-1}}{c^3 (n+1) (2 n+1) (3 n+1)}+\frac{6 a^3 n^3 x \left(c+d x^n\right)^{-1/n}}{c^4 (n+1) (2 n+1) (3 n+1)}+\frac{3 a n x \left(a+b x^n\right)^2 \left(c+d x^n\right)^{-\frac{1}{n}-2}}{c^2 \left(6 n^2+5 n+1\right)}+\frac{x \left(a+b x^n\right)^3 \left(c+d x^n\right)^{-\frac{1}{n}-3}}{c (3 n+1)}","\frac{6 a^2 n^2 x \left(a+b x^n\right) \left(c+d x^n\right)^{-\frac{1}{n}-1}}{c^3 (n+1) (2 n+1) (3 n+1)}+\frac{6 a^3 n^3 x \left(c+d x^n\right)^{-1/n}}{c^4 (n+1) (2 n+1) (3 n+1)}+\frac{3 a n x \left(a+b x^n\right)^2 \left(c+d x^n\right)^{-\frac{1}{n}-2}}{c^2 \left(6 n^2+5 n+1\right)}+\frac{x \left(a+b x^n\right)^3 \left(c+d x^n\right)^{-\frac{1}{n}-3}}{c (3 n+1)}",1,"(x*(a + b*x^n)^3*(c + d*x^n)^(-3 - n^(-1)))/(c*(1 + 3*n)) + (3*a*n*x*(a + b*x^n)^2*(c + d*x^n)^(-2 - n^(-1)))/(c^2*(1 + 5*n + 6*n^2)) + (6*a^2*n^2*x*(a + b*x^n)*(c + d*x^n)^(-1 - n^(-1)))/(c^3*(1 + n)*(1 + 2*n)*(1 + 3*n)) + (6*a^3*n^3*x)/(c^4*(1 + n)*(1 + 2*n)*(1 + 3*n)*(c + d*x^n)^n^(-1))","A",4,2,25,0.08000,1,"{378, 191}"
322,1,116,0,0.0360545,"\int \left(a+b x^n\right)^2 \left(c+d x^n\right)^{-3-\frac{1}{n}} \, dx","Int[(a + b*x^n)^2*(c + d*x^n)^(-3 - n^(-1)),x]","\frac{2 a^2 n^2 x \left(c+d x^n\right)^{-1/n}}{c^3 (n+1) (2 n+1)}+\frac{2 a n x \left(a+b x^n\right) \left(c+d x^n\right)^{-\frac{1}{n}-1}}{c^2 (n+1) (2 n+1)}+\frac{x \left(a+b x^n\right)^2 \left(c+d x^n\right)^{-\frac{1}{n}-2}}{c (2 n+1)}","\frac{2 a^2 n^2 x \left(c+d x^n\right)^{-1/n}}{c^3 (n+1) (2 n+1)}+\frac{2 a n x \left(a+b x^n\right) \left(c+d x^n\right)^{-\frac{1}{n}-1}}{c^2 (n+1) (2 n+1)}+\frac{x \left(a+b x^n\right)^2 \left(c+d x^n\right)^{-\frac{1}{n}-2}}{c (2 n+1)}",1,"(x*(a + b*x^n)^2*(c + d*x^n)^(-2 - n^(-1)))/(c*(1 + 2*n)) + (2*a*n*x*(a + b*x^n)*(c + d*x^n)^(-1 - n^(-1)))/(c^2*(1 + n)*(1 + 2*n)) + (2*a^2*n^2*x)/(c^3*(1 + n)*(1 + 2*n)*(c + d*x^n)^n^(-1))","A",3,2,25,0.08000,1,"{378, 191}"
323,1,58,0,0.0136548,"\int \left(a+b x^n\right) \left(c+d x^n\right)^{-2-\frac{1}{n}} \, dx","Int[(a + b*x^n)*(c + d*x^n)^(-2 - n^(-1)),x]","\frac{x \left(a+b x^n\right) \left(c+d x^n\right)^{-\frac{1}{n}-1}}{c (n+1)}+\frac{a n x \left(c+d x^n\right)^{-1/n}}{c^2 (n+1)}","\frac{x \left(a+b x^n\right) \left(c+d x^n\right)^{-\frac{1}{n}-1}}{c (n+1)}+\frac{a n x \left(c+d x^n\right)^{-1/n}}{c^2 (n+1)}",1,"(x*(a + b*x^n)*(c + d*x^n)^(-1 - n^(-1)))/(c*(1 + n)) + (a*n*x)/(c^2*(1 + n)*(c + d*x^n)^n^(-1))","A",2,2,23,0.08696,1,"{378, 191}"
324,1,18,0,0.0026634,"\int \left(c+d x^n\right)^{-1-\frac{1}{n}} \, dx","Int[(c + d*x^n)^(-1 - n^(-1)),x]","\frac{x \left(c+d x^n\right)^{-1/n}}{c}","\frac{x \left(c+d x^n\right)^{-1/n}}{c}",1,"x/(c*(c + d*x^n)^n^(-1))","A",1,1,15,0.06667,1,"{191}"
325,1,53,0,0.0139553,"\int \frac{\left(c+d x^n\right)^{-1/n}}{a+b x^n} \, dx","Int[1/((a + b*x^n)*(c + d*x^n)^n^(-1)),x]","\frac{x \left(c+d x^n\right)^{-1/n} \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a}","\frac{x \left(c+d x^n\right)^{-1/n} \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a}",1,"(x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/(a*(c + d*x^n)^n^(-1))","A",1,1,23,0.04348,1,"{379}"
326,1,54,0,0.0136726,"\int \frac{\left(c+d x^n\right)^{1-\frac{1}{n}}}{\left(a+b x^n\right)^2} \, dx","Int[(c + d*x^n)^(1 - n^(-1))/(a + b*x^n)^2,x]","\frac{c x \left(c+d x^n\right)^{-1/n} \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a^2}","\frac{c x \left(c+d x^n\right)^{-1/n} \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a^2}",1,"(c*x*Hypergeometric2F1[2, n^(-1), 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/(a^2*(c + d*x^n)^n^(-1))","A",1,1,25,0.04000,1,"{379}"
327,1,56,0,0.0151126,"\int \frac{\left(c+d x^n\right)^{2-\frac{1}{n}}}{\left(a+b x^n\right)^3} \, dx","Int[(c + d*x^n)^(2 - n^(-1))/(a + b*x^n)^3,x]","\frac{c^2 x \left(c+d x^n\right)^{-1/n} \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a^3}","\frac{c^2 x \left(c+d x^n\right)^{-1/n} \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a^3}",1,"(c^2*x*Hypergeometric2F1[3, n^(-1), 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/(a^3*(c + d*x^n)^n^(-1))","A",1,1,25,0.04000,1,"{379}"
328,1,179,0,0.0812199,"\int \left(a+b x^n\right)^p \left(c+d x^n\right)^{-2-\frac{1}{n}-p} \, dx","Int[(a + b*x^n)^p*(c + d*x^n)^(-2 - n^(-1) - p),x]","\frac{x \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{-\frac{1}{n}-p-1} \left(\frac{b}{n (p+1) (b c-a d)}+\frac{1}{c}\right) \left(\frac{c \left(a+b x^n\right)}{a \left(c+d x^n\right)}\right)^{-p-1} \, _2F_1\left(\frac{1}{n},-p-1;1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a}-\frac{b x \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{-\frac{1}{n}-p-1}}{a n (p+1) (b c-a d)}","\frac{x \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{-\frac{1}{n}-p-1} (n (p+1) (b c-a d)+b c) \left(\frac{c \left(a+b x^n\right)}{a \left(c+d x^n\right)}\right)^{-p-1} \, _2F_1\left(\frac{1}{n},-p-1;1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a c n (p+1) (b c-a d)}-\frac{b x \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{-\frac{1}{n}-p-1}}{a n (p+1) (b c-a d)}",1,"-((b*x*(a + b*x^n)^(1 + p)*(c + d*x^n)^(-1 - n^(-1) - p))/(a*(b*c - a*d)*n*(1 + p))) + ((c^(-1) + b/((b*c - a*d)*n*(1 + p)))*x*(a + b*x^n)^(1 + p)*((c*(a + b*x^n))/(a*(c + d*x^n)))^(-1 - p)*(c + d*x^n)^(-1 - n^(-1) - p)*Hypergeometric2F1[n^(-1), -1 - p, 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/a","A",2,2,28,0.07143,1,"{382, 380}"
329,1,57,0,0.0271107,"\int \left(a+b x^n\right)^{\frac{a d n-b c (1+n)}{(b c-a d) n}} \left(c+d x^n\right)^{\frac{a d-b c n+a d n}{b c n-a d n}} \, dx","Int[(a + b*x^n)^((a*d*n - b*c*(1 + n))/((b*c - a*d)*n))*(c + d*x^n)^((a*d - b*c*n + a*d*n)/(b*c*n - a*d*n)),x]","\frac{x \left(a+b x^n\right)^{-\frac{b c}{n (b c-a d)}} \left(c+d x^n\right)^{\frac{a d}{n (b c-a d)}}}{a c}","\frac{x \left(a+b x^n\right)^{-\frac{b c}{n (b c-a d)}} \left(c+d x^n\right)^{\frac{a d}{n (b c-a d)}}}{a c}",1,"(x*(c + d*x^n)^((a*d)/((b*c - a*d)*n)))/(a*c*(a + b*x^n)^((b*c)/((b*c - a*d)*n)))","A",1,1,69,0.01449,1,"{381}"
330,1,327,0,0.184194,"\int \left(a+b x^n\right)^2 \left(c+d x^n\right)^{-4-\frac{1}{n}} \, dx","Int[(a + b*x^n)^2*(c + d*x^n)^(-4 - n^(-1)),x]","-\frac{2 a^2 n^2 x \left(c+d x^n\right)^{-1/n} (3 a d n-b (3 c n+c))}{c^4 (n+1) (2 n+1) (3 n+1) (b c-a d)}-\frac{x \left(a+b x^n\right)^2 \left(c+d x^n\right)^{-\frac{1}{n}-2} (3 a d n-b (3 c n+c))}{c^2 \left(6 n^2+5 n+1\right) (b c-a d)}-\frac{2 a n x \left(a+b x^n\right) \left(c+d x^n\right)^{-\frac{1}{n}-1} (3 a d n-b (3 c n+c))}{c^3 (n+1) (2 n+1) (3 n+1) (b c-a d)}-\frac{x \left(a+b x^n\right)^3 \left(c+d x^n\right)^{-\frac{1}{n}-3} (3 a d n-b (3 c n+c))}{3 a c n (3 n+1) (b c-a d)}-\frac{b x \left(a+b x^n\right)^3 \left(c+d x^n\right)^{-\frac{1}{n}-3}}{3 a n (b c-a d)}","-\frac{2 a^2 n^2 x \left(c+d x^n\right)^{-1/n} (3 a d n-b (3 c n+c))}{c^4 (n+1) (2 n+1) (3 n+1) (b c-a d)}-\frac{x \left(a+b x^n\right)^2 \left(c+d x^n\right)^{-\frac{1}{n}-2} (3 a d n-b (3 c n+c))}{c^2 \left(6 n^2+5 n+1\right) (b c-a d)}-\frac{2 a n x \left(a+b x^n\right) \left(c+d x^n\right)^{-\frac{1}{n}-1} (3 a d n-b (3 c n+c))}{c^3 (n+1) (2 n+1) (3 n+1) (b c-a d)}-\frac{x \left(a+b x^n\right)^3 \left(c+d x^n\right)^{-\frac{1}{n}-3} (3 a d n-b (3 c n+c))}{3 a c n (3 n+1) (b c-a d)}-\frac{b x \left(a+b x^n\right)^3 \left(c+d x^n\right)^{-\frac{1}{n}-3}}{3 a n (b c-a d)}",1,"-(b*x*(a + b*x^n)^3*(c + d*x^n)^(-3 - n^(-1)))/(3*a*(b*c - a*d)*n) - ((3*a*d*n - b*(c + 3*c*n))*x*(a + b*x^n)^3*(c + d*x^n)^(-3 - n^(-1)))/(3*a*c*(b*c - a*d)*n*(1 + 3*n)) - ((3*a*d*n - b*(c + 3*c*n))*x*(a + b*x^n)^2*(c + d*x^n)^(-2 - n^(-1)))/(c^2*(b*c - a*d)*(1 + 5*n + 6*n^2)) - (2*a*n*(3*a*d*n - b*(c + 3*c*n))*x*(a + b*x^n)*(c + d*x^n)^(-1 - n^(-1)))/(c^3*(b*c - a*d)*(1 + n)*(1 + 2*n)*(1 + 3*n)) - (2*a^2*n^2*(3*a*d*n - b*(c + 3*c*n))*x)/(c^4*(b*c - a*d)*(1 + n)*(1 + 2*n)*(1 + 3*n)*(c + d*x^n)^n^(-1))","A",5,3,25,0.1200,1,"{382, 378, 191}"
331,1,127,0,0.063562,"\int \left(a+b x^n\right) \left(c+d x^n\right)^{-3-\frac{1}{n}} \, dx","Int[(a + b*x^n)*(c + d*x^n)^(-3 - n^(-1)),x]","\frac{x \left(c+d x^n\right)^{-\frac{1}{n}-1} (2 a d n+b c)}{c^2 d (n+1) (2 n+1)}+\frac{n x \left(c+d x^n\right)^{-1/n} (2 a d n+b c)}{c^3 d (n+1) (2 n+1)}-\frac{x (b c-a d) \left(c+d x^n\right)^{-\frac{1}{n}-2}}{c d (2 n+1)}","\frac{x \left(c+d x^n\right)^{-\frac{1}{n}-1} (2 a d n+b c)}{c^2 d (n+1) (2 n+1)}+\frac{n x \left(c+d x^n\right)^{-1/n} (2 a d n+b c)}{c^3 d (n+1) (2 n+1)}-\frac{x (b c-a d) \left(c+d x^n\right)^{-\frac{1}{n}-2}}{c d (2 n+1)}",1,"-(((b*c - a*d)*x*(c + d*x^n)^(-2 - n^(-1)))/(c*d*(1 + 2*n))) + ((b*c + 2*a*d*n)*x*(c + d*x^n)^(-1 - n^(-1)))/(c^2*d*(1 + n)*(1 + 2*n)) + (n*(b*c + 2*a*d*n)*x)/(c^3*d*(1 + n)*(1 + 2*n)*(c + d*x^n)^n^(-1))","A",3,3,23,0.1304,1,"{385, 192, 191}"
332,1,50,0,0.0123664,"\int \left(c+d x^n\right)^{-2-\frac{1}{n}} \, dx","Int[(c + d*x^n)^(-2 - n^(-1)),x]","\frac{n x \left(c+d x^n\right)^{-1/n}}{c^2 (n+1)}+\frac{x \left(c+d x^n\right)^{-\frac{1}{n}-1}}{c (n+1)}","\frac{n x \left(c+d x^n\right)^{-1/n}}{c^2 (n+1)}+\frac{x \left(c+d x^n\right)^{-\frac{1}{n}-1}}{c (n+1)}",1,"(x*(c + d*x^n)^(-1 - n^(-1)))/(c*(1 + n)) + (n*x)/(c^2*(1 + n)*(c + d*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{192, 191}"
333,1,95,0,0.0313336,"\int \frac{\left(c+d x^n\right)^{-1-\frac{1}{n}}}{a+b x^n} \, dx","Int[(c + d*x^n)^(-1 - n^(-1))/(a + b*x^n),x]","\frac{b x \left(c+d x^n\right)^{-1/n} \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a (b c-a d)}-\frac{d x \left(c+d x^n\right)^{-1/n}}{c (b c-a d)}","\frac{b x \left(c+d x^n\right)^{-1/n} \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a (b c-a d)}-\frac{d x \left(c+d x^n\right)^{-1/n}}{c (b c-a d)}",1,"-((d*x)/(c*(b*c - a*d)*(c + d*x^n)^n^(-1))) + (b*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/(a*(b*c - a*d)*(c + d*x^n)^n^(-1))","A",2,2,25,0.08000,1,"{382, 379}"
334,1,127,0,0.0522504,"\int \frac{\left(c+d x^n\right)^{-1/n}}{\left(a+b x^n\right)^2} \, dx","Int[1/((a + b*x^n)^2*(c + d*x^n)^n^(-1)),x]","\frac{b x \left(c+d x^n\right)^{-\frac{1-n}{n}}}{a n (b c-a d) \left(a+b x^n\right)}-\frac{x \left(c+d x^n\right)^{-1/n} (a d n+b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a^2 n (b c-a d)}","\frac{b x \left(c+d x^n\right)^{-\frac{1-n}{n}}}{a n (b c-a d) \left(a+b x^n\right)}-\frac{x \left(c+d x^n\right)^{-1/n} (a d n+b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{a^2 n (b c-a d)}",1,"(b*x)/(a*(b*c - a*d)*n*(a + b*x^n)*(c + d*x^n)^((1 - n)/n)) - ((b*c*(1 - n) + a*d*n)*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/(a^2*(b*c - a*d)*n*(c + d*x^n)^n^(-1))","A",2,2,23,0.08696,1,"{382, 379}"
335,1,131,0,0.0557339,"\int \frac{\left(c+d x^n\right)^{1-\frac{1}{n}}}{\left(a+b x^n\right)^3} \, dx","Int[(c + d*x^n)^(1 - n^(-1))/(a + b*x^n)^3,x]","\frac{b x \left(c+d x^n\right)^{2-\frac{1}{n}}}{2 a n (b c-a d) \left(a+b x^n\right)^2}-\frac{c x \left(c+d x^n\right)^{-1/n} (2 a d n+b c (1-2 n)) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{2 a^3 n (b c-a d)}","\frac{b x \left(c+d x^n\right)^{2-\frac{1}{n}}}{2 a n (b c-a d) \left(a+b x^n\right)^2}-\frac{c x \left(c+d x^n\right)^{-1/n} (2 a d n+b c (1-2 n)) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{2 a^3 n (b c-a d)}",1,"(b*x*(c + d*x^n)^(2 - n^(-1)))/(2*a*(b*c - a*d)*n*(a + b*x^n)^2) - (c*(b*c*(1 - 2*n) + 2*a*d*n)*x*Hypergeometric2F1[2, n^(-1), 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/(2*a^3*(b*c - a*d)*n*(c + d*x^n)^n^(-1))","A",2,2,25,0.08000,1,"{382, 379}"
336,1,133,0,0.0546743,"\int \frac{\left(c+d x^n\right)^{2-\frac{1}{n}}}{\left(a+b x^n\right)^4} \, dx","Int[(c + d*x^n)^(2 - n^(-1))/(a + b*x^n)^4,x]","\frac{b x \left(c+d x^n\right)^{3-\frac{1}{n}}}{3 a n (b c-a d) \left(a+b x^n\right)^3}-\frac{c^2 x \left(c+d x^n\right)^{-1/n} (3 a d n+b c (1-3 n)) \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{3 a^4 n (b c-a d)}","\frac{b x \left(c+d x^n\right)^{3-\frac{1}{n}}}{3 a n (b c-a d) \left(a+b x^n\right)^3}-\frac{c^2 x \left(c+d x^n\right)^{-1/n} (3 a d n+b c (1-3 n)) \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{(b c-a d) x^n}{a \left(d x^n+c\right)}\right)}{3 a^4 n (b c-a d)}",1,"(b*x*(c + d*x^n)^(3 - n^(-1)))/(3*a*(b*c - a*d)*n*(a + b*x^n)^3) - (c^2*(b*c*(1 - 3*n) + 3*a*d*n)*x*Hypergeometric2F1[3, n^(-1), 1 + n^(-1), -(((b*c - a*d)*x^n)/(a*(c + d*x^n)))])/(3*a^4*(b*c - a*d)*n*(c + d*x^n)^n^(-1))","A",2,2,25,0.08000,1,"{382, 379}"
337,1,164,0,0.1180743,"\int x^5 \sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right) \, dx","Int[x^5*Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2),x]","\frac{x^4 (d x-c)^{3/2} (c+d x)^{3/2} \left(3 a d^2+2 b c^2\right)}{21 d^4}+\frac{4 c^2 x^2 (d x-c)^{3/2} (c+d x)^{3/2} \left(3 a d^2+2 b c^2\right)}{105 d^6}+\frac{8 c^4 (d x-c)^{3/2} (c+d x)^{3/2} \left(3 a d^2+2 b c^2\right)}{315 d^8}+\frac{b x^6 (d x-c)^{3/2} (c+d x)^{3/2}}{9 d^2}","\frac{(d x-c)^{7/2} (c+d x)^{7/2} \left(a d^2+3 b c^2\right)}{7 d^8}+\frac{c^2 (d x-c)^{5/2} (c+d x)^{5/2} \left(2 a d^2+3 b c^2\right)}{5 d^8}+\frac{c^4 (d x-c)^{3/2} (c+d x)^{3/2} \left(a d^2+b c^2\right)}{3 d^8}+\frac{b (d x-c)^{9/2} (c+d x)^{9/2}}{9 d^8}",1,"(8*c^4*(2*b*c^2 + 3*a*d^2)*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(315*d^8) + (4*c^2*(2*b*c^2 + 3*a*d^2)*x^2*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(105*d^6) + ((2*b*c^2 + 3*a*d^2)*x^4*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(21*d^4) + (b*x^6*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(9*d^2)","A",6,4,31,0.1290,1,"{460, 100, 12, 74}"
338,1,118,0,0.0867472,"\int x^3 \sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right) \, dx","Int[x^3*Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2),x]","\frac{x^2 (d x-c)^{3/2} (c+d x)^{3/2} \left(7 a d^2+4 b c^2\right)}{35 d^4}+\frac{2 c^2 (d x-c)^{3/2} (c+d x)^{3/2} \left(7 a d^2+4 b c^2\right)}{105 d^6}+\frac{b x^4 (d x-c)^{3/2} (c+d x)^{3/2}}{7 d^2}","\frac{(d x-c)^{5/2} (c+d x)^{5/2} \left(a d^2+2 b c^2\right)}{5 d^6}+\frac{c^2 (d x-c)^{3/2} (c+d x)^{3/2} \left(a d^2+b c^2\right)}{3 d^6}+\frac{b (d x-c)^{7/2} (c+d x)^{7/2}}{7 d^6}",1,"(2*c^2*(4*b*c^2 + 7*a*d^2)*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(105*d^6) + ((4*b*c^2 + 7*a*d^2)*x^2*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(35*d^4) + (b*x^4*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(7*d^2)","A",4,4,31,0.1290,1,"{460, 100, 12, 74}"
339,1,72,0,0.0443008,"\int x \sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right) \, dx","Int[x*Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2),x]","\frac{(d x-c)^{3/2} (c+d x)^{3/2} \left(5 a d^2+2 b c^2\right)}{15 d^4}+\frac{b x^2 (d x-c)^{3/2} (c+d x)^{3/2}}{5 d^2}","\frac{(d x-c)^{3/2} (c+d x)^{3/2} \left(a d^2+b c^2\right)}{3 d^4}+\frac{b (d x-c)^{5/2} (c+d x)^{5/2}}{5 d^4}",1,"((2*b*c^2 + 5*a*d^2)*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(15*d^4) + (b*x^2*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(5*d^2)","A",2,2,29,0.06897,1,"{460, 74}"
340,1,80,0,0.0782181,"\int \frac{\sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right)}{x} \, dx","Int[(Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2))/x,x]","a \sqrt{d x-c} \sqrt{c+d x}-a c \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)+\frac{b (d x-c)^{3/2} (c+d x)^{3/2}}{3 d^2}","a \sqrt{d x-c} \sqrt{c+d x}-a c \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)+\frac{b (d x-c)^{3/2} (c+d x)^{3/2}}{3 d^2}",1,"a*Sqrt[-c + d*x]*Sqrt[c + d*x] + (b*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(3*d^2) - a*c*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c]","A",5,5,31,0.1613,1,"{460, 101, 12, 92, 205}"
341,1,114,0,0.0840813,"\int \frac{\sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right)}{x^3} \, dx","Int[(Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2))/x^3,x]","\frac{1}{2} \sqrt{d x-c} \sqrt{c+d x} \left(2 b-\frac{a d^2}{c^2}\right)-\frac{\left(2 b c^2-a d^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{2 c}+\frac{a (d x-c)^{3/2} (c+d x)^{3/2}}{2 c^2 x^2}","-\frac{\left(2 b c^2-a d^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{2 c}-\frac{a \sqrt{d x-c} \sqrt{c+d x}}{2 x^2}+b \sqrt{d x-c} \sqrt{c+d x}",1,"((2*b - (a*d^2)/c^2)*Sqrt[-c + d*x]*Sqrt[c + d*x])/2 + (a*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(2*c^2*x^2) - ((2*b*c^2 - a*d^2)*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c])/(2*c)","A",5,5,31,0.1613,1,"{454, 101, 12, 92, 205}"
342,1,164,0,0.1035937,"\int \frac{\sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right)}{x^5} \, dx","Int[(Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2))/x^5,x]","-\frac{\sqrt{d x-c} (c+d x)^{3/2} \left(a d^2+4 b c^2\right)}{8 c^3 x^2}+\frac{d \sqrt{d x-c} \sqrt{c+d x} \left(a d^2+4 b c^2\right)}{8 c^3 x}+\frac{d^2 \left(a d^2+4 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{8 c^3}+\frac{a (d x-c)^{3/2} (c+d x)^{3/2}}{4 c^2 x^4}","-\frac{\sqrt{d x-c} \sqrt{c+d x} \left(a d^2+4 b c^2\right)}{8 c^2 x^2}+\frac{d^2 \left(a d^2+4 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{8 c^3}+\frac{a (d x-c)^{3/2} (c+d x)^{3/2}}{4 c^2 x^4}",1,"(d*(4*b*c^2 + a*d^2)*Sqrt[-c + d*x]*Sqrt[c + d*x])/(8*c^3*x) - ((4*b*c^2 + a*d^2)*Sqrt[-c + d*x]*(c + d*x)^(3/2))/(8*c^3*x^2) + (a*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(4*c^2*x^4) + (d^2*(4*b*c^2 + a*d^2)*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c])/(8*c^3)","A",5,4,31,0.1290,1,"{454, 94, 92, 205}"
343,1,208,0,0.1488837,"\int x^4 \sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right) \, dx","Int[x^4*Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2),x]","\frac{x^3 (d x-c)^{3/2} (c+d x)^{3/2} \left(8 a d^2+5 b c^2\right)}{48 d^4}+\frac{c^4 x \sqrt{d x-c} \sqrt{c+d x} \left(8 a d^2+5 b c^2\right)}{128 d^6}+\frac{c^2 x (d x-c)^{3/2} (c+d x)^{3/2} \left(8 a d^2+5 b c^2\right)}{64 d^6}-\frac{c^6 \left(8 a d^2+5 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{64 d^7}+\frac{b x^5 (d x-c)^{3/2} (c+d x)^{3/2}}{8 d^2}","\frac{x^3 (d x-c)^{3/2} (c+d x)^{3/2} \left(8 a d^2+5 b c^2\right)}{48 d^4}+\frac{c^4 x \sqrt{d x-c} \sqrt{c+d x} \left(8 a d^2+5 b c^2\right)}{128 d^6}+\frac{c^2 x (d x-c)^{3/2} (c+d x)^{3/2} \left(8 a d^2+5 b c^2\right)}{64 d^6}-\frac{c^6 \left(8 a d^2+5 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{64 d^7}+\frac{b x^5 (d x-c)^{3/2} (c+d x)^{3/2}}{8 d^2}",1,"(c^4*(5*b*c^2 + 8*a*d^2)*x*Sqrt[-c + d*x]*Sqrt[c + d*x])/(128*d^6) + (c^2*(5*b*c^2 + 8*a*d^2)*x*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(64*d^6) + ((5*b*c^2 + 8*a*d^2)*x^3*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(48*d^4) + (b*x^5*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(8*d^2) - (c^6*(5*b*c^2 + 8*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/(64*d^7)","A",9,8,31,0.2581,1,"{460, 100, 12, 90, 38, 63, 217, 206}"
344,1,159,0,0.1234543,"\int x^2 \sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right) \, dx","Int[x^2*Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2),x]","\frac{c^2 x \sqrt{d x-c} \sqrt{c+d x} \left(2 a d^2+b c^2\right)}{16 d^4}+\frac{x (d x-c)^{3/2} (c+d x)^{3/2} \left(2 a d^2+b c^2\right)}{8 d^4}-\frac{c^4 \left(2 a d^2+b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{8 d^5}+\frac{b x^3 (d x-c)^{3/2} (c+d x)^{3/2}}{6 d^2}","\frac{c^2 x \sqrt{d x-c} \sqrt{c+d x} \left(2 a d^2+b c^2\right)}{16 d^4}+\frac{x (d x-c)^{3/2} (c+d x)^{3/2} \left(2 a d^2+b c^2\right)}{8 d^4}-\frac{c^4 \left(2 a d^2+b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{8 d^5}+\frac{b x^3 (d x-c)^{3/2} (c+d x)^{3/2}}{6 d^2}",1,"(c^2*(b*c^2 + 2*a*d^2)*x*Sqrt[-c + d*x]*Sqrt[c + d*x])/(16*d^4) + ((b*c^2 + 2*a*d^2)*x*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(8*d^4) + (b*x^3*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(6*d^2) - (c^4*(b*c^2 + 2*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/(8*d^5)","A",7,7,31,0.2258,1,"{460, 90, 12, 38, 63, 217, 206}"
345,1,114,0,0.0465434,"\int \sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right) \, dx","Int[Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2),x]","\frac{x \sqrt{d x-c} \sqrt{c+d x} \left(4 a d^2+b c^2\right)}{8 d^2}-\frac{c^2 \left(4 a d^2+b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{4 d^3}+\frac{b x (d x-c)^{3/2} (c+d x)^{3/2}}{4 d^2}","\frac{x \sqrt{d x-c} \sqrt{c+d x} \left(4 a d^2+b c^2\right)}{8 d^2}-\frac{c^2 \left(4 a d^2+b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{4 d^3}+\frac{b x (d x-c)^{3/2} (c+d x)^{3/2}}{4 d^2}",1,"((b*c^2 + 4*a*d^2)*x*Sqrt[-c + d*x]*Sqrt[c + d*x])/(8*d^2) + (b*x*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(4*d^2) - (c^2*(b*c^2 + 4*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/(4*d^3)","A",5,5,28,0.1786,1,"{389, 38, 63, 217, 206}"
346,1,104,0,0.0869517,"\int \frac{\sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right)}{x^2} \, dx","Int[(Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2))/x^2,x]","\frac{1}{2} x \sqrt{d x-c} \sqrt{c+d x} \left(b-\frac{2 a d^2}{c^2}\right)-\frac{\left(b c^2-2 a d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d}+\frac{a (d x-c)^{3/2} (c+d x)^{3/2}}{c^2 x}","\frac{1}{2} x \sqrt{d x-c} \sqrt{c+d x} \left(b-\frac{2 a d^2}{c^2}\right)-\frac{\left(b c^2-2 a d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d}+\frac{a (d x-c)^{3/2} (c+d x)^{3/2}}{c^2 x}",1,"((b - (2*a*d^2)/c^2)*x*Sqrt[-c + d*x]*Sqrt[c + d*x])/2 + (a*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(c^2*x) - ((b*c^2 - 2*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/d","A",5,5,31,0.1613,1,"{454, 38, 63, 217, 206}"
347,1,84,0,0.0803436,"\int \frac{\sqrt{-c+d x} \sqrt{c+d x} \left(a+b x^2\right)}{x^4} \, dx","Int[(Sqrt[-c + d*x]*Sqrt[c + d*x]*(a + b*x^2))/x^4,x]","\frac{a (d x-c)^{3/2} (c+d x)^{3/2}}{3 c^2 x^3}-\frac{b \sqrt{d x-c} \sqrt{c+d x}}{x}+2 b d \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)","\frac{a (d x-c)^{3/2} (c+d x)^{3/2}}{3 c^2 x^3}-\frac{b \sqrt{d x-c} \sqrt{c+d x}}{x}+2 b d \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)",1,"-((b*Sqrt[-c + d*x]*Sqrt[c + d*x])/x) + (a*(-c + d*x)^(3/2)*(c + d*x)^(3/2))/(3*c^2*x^3) + 2*b*d*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]]","A",6,6,31,0.1935,1,"{454, 97, 12, 63, 217, 206}"
348,1,125,0,0.0848769,"\int \frac{x^4 \left(a+b x^2\right)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(x^4*(a + b*x^2))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{x^3 \sqrt{c x-1} \sqrt{c x+1} \left(6 a c^2+5 b\right)}{24 c^4}+\frac{x \sqrt{c x-1} \sqrt{c x+1} \left(6 a c^2+5 b\right)}{16 c^6}+\frac{\left(6 a c^2+5 b\right) \cosh ^{-1}(c x)}{16 c^7}+\frac{b x^5 \sqrt{c x-1} \sqrt{c x+1}}{6 c^2}","\frac{x^3 \sqrt{c x-1} \sqrt{c x+1} \left(6 a c^2+5 b\right)}{24 c^4}+\frac{x \sqrt{c x-1} \sqrt{c x+1} \left(6 a c^2+5 b\right)}{16 c^6}+\frac{\left(6 a c^2+5 b\right) \cosh ^{-1}(c x)}{16 c^7}+\frac{b x^5 \sqrt{c x-1} \sqrt{c x+1}}{6 c^2}",1,"((5*b + 6*a*c^2)*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*c^6) + ((5*b + 6*a*c^2)*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(24*c^4) + (b*x^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*c^2) + ((5*b + 6*a*c^2)*ArcCosh[c*x])/(16*c^7)","A",5,5,29,0.1724,1,"{460, 100, 12, 90, 52}"
349,1,103,0,0.0749051,"\int \frac{x^3 \left(a+b x^2\right)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(x^3*(a + b*x^2))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{x^2 \sqrt{c x-1} \sqrt{c x+1} \left(5 a c^2+4 b\right)}{15 c^4}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \left(5 a c^2+4 b\right)}{15 c^6}+\frac{b x^4 \sqrt{c x-1} \sqrt{c x+1}}{5 c^2}","\frac{x^2 \sqrt{c x-1} \sqrt{c x+1} \left(5 a c^2+4 b\right)}{15 c^4}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \left(5 a c^2+4 b\right)}{15 c^6}+\frac{b x^4 \sqrt{c x-1} \sqrt{c x+1}}{5 c^2}",1,"(2*(4*b + 5*a*c^2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(15*c^6) + ((4*b + 5*a*c^2)*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(15*c^4) + (b*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(5*c^2)","A",4,4,29,0.1379,1,"{460, 100, 12, 74}"
350,1,87,0,0.0694708,"\int \frac{x^2 \left(a+b x^2\right)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(x^2*(a + b*x^2))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{x \sqrt{c x-1} \sqrt{c x+1} \left(4 a c^2+3 b\right)}{8 c^4}+\frac{\left(4 a c^2+3 b\right) \cosh ^{-1}(c x)}{8 c^5}+\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1}}{4 c^2}","\frac{x \sqrt{c x-1} \sqrt{c x+1} \left(4 a c^2+3 b\right)}{8 c^4}+\frac{\left(4 a c^2+3 b\right) \cosh ^{-1}(c x)}{8 c^5}+\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1}}{4 c^2}",1,"((3*b + 4*a*c^2)*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(8*c^4) + (b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c^2) + ((3*b + 4*a*c^2)*ArcCosh[c*x])/(8*c^5)","A",3,3,29,0.1034,1,"{460, 90, 52}"
351,1,65,0,0.0402388,"\int \frac{x \left(a+b x^2\right)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(x*(a + b*x^2))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(3 a c^2+2 b\right)}{3 c^4}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{3 c^2}","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(3 a c^2+2 b\right)}{3 c^4}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{3 c^2}",1,"((2*b + 3*a*c^2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*c^4) + (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*c^2)","A",2,2,27,0.07407,1,"{460, 74}"
352,1,47,0,0.0195731,"\int \frac{a+b x^2}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(a + b*x^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{\left(2 a c^2+b\right) \cosh ^{-1}(c x)}{2 c^3}+\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{2 c^2}","\frac{\left(2 a c^2+b\right) \cosh ^{-1}(c x)}{2 c^3}+\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{2 c^2}",1,"(b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*c^2) + ((b + 2*a*c^2)*ArcCosh[c*x])/(2*c^3)","A",2,2,26,0.07692,1,"{389, 52}"
353,1,46,0,0.0612882,"\int \frac{a+b x^2}{x \sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(a + b*x^2)/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","a \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{c^2}","a \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{c^2}",1,"(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/c^2 + a*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]]","A",3,3,29,0.1034,1,"{460, 92, 205}"
354,1,33,0,0.0565493,"\int \frac{a+b x^2}{x^2 \sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(a + b*x^2)/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{a \sqrt{c x-1} \sqrt{c x+1}}{x}+\frac{b \cosh ^{-1}(c x)}{c}","\frac{a \sqrt{c x-1} \sqrt{c x+1}}{x}+\frac{b \cosh ^{-1}(c x)}{c}",1,"(a*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/x + (b*ArcCosh[c*x])/c","A",2,2,29,0.06897,1,"{454, 52}"
355,1,60,0,0.0630479,"\int \frac{a+b x^2}{x^3 \sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(a + b*x^2)/(x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{1}{2} \left(a c^2+2 b\right) \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{a \sqrt{c x-1} \sqrt{c x+1}}{2 x^2}","\frac{1}{2} \left(a c^2+2 b\right) \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{a \sqrt{c x-1} \sqrt{c x+1}}{2 x^2}",1,"(a*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*x^2) + ((2*b + a*c^2)*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/2","A",3,3,29,0.1034,1,"{454, 92, 205}"
356,1,62,0,0.0623655,"\int \frac{a+b x^2}{x^4 \sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(a + b*x^2)/(x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(2 a c^2+3 b\right)}{3 x}+\frac{a \sqrt{c x-1} \sqrt{c x+1}}{3 x^3}","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(2 a c^2+3 b\right)}{3 x}+\frac{a \sqrt{c x-1} \sqrt{c x+1}}{3 x^3}",1,"(a*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*x^3) + ((3*b + 2*a*c^2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*x)","A",2,2,29,0.06897,1,"{454, 95}"
357,1,99,0,0.0780453,"\int \frac{a+b x^2}{x^5 \sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(a + b*x^2)/(x^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(3 a c^2+4 b\right)}{8 x^2}+\frac{1}{8} c^2 \left(3 a c^2+4 b\right) \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{a \sqrt{c x-1} \sqrt{c x+1}}{4 x^4}","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(3 a c^2+4 b\right)}{8 x^2}+\frac{1}{8} c^2 \left(3 a c^2+4 b\right) \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{a \sqrt{c x-1} \sqrt{c x+1}}{4 x^4}",1,"(a*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*x^4) + ((4*b + 3*a*c^2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(8*x^2) + (c^2*(4*b + 3*a*c^2)*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/8","A",5,5,29,0.1724,1,"{454, 103, 12, 92, 205}"
358,1,164,0,0.1197335,"\int \frac{x^4 \left(a+b x^2\right)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(x^4*(a + b*x^2))/(Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{x^3 \sqrt{d x-c} \sqrt{c+d x} \left(6 a d^2+5 b c^2\right)}{24 d^4}+\frac{c^2 x \sqrt{d x-c} \sqrt{c+d x} \left(6 a d^2+5 b c^2\right)}{16 d^6}+\frac{c^4 \left(6 a d^2+5 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{8 d^7}+\frac{b x^5 \sqrt{d x-c} \sqrt{c+d x}}{6 d^2}","\frac{x^3 \sqrt{d x-c} \sqrt{c+d x} \left(6 a d^2+5 b c^2\right)}{24 d^4}+\frac{c^2 x \sqrt{d x-c} \sqrt{c+d x} \left(6 a d^2+5 b c^2\right)}{16 d^6}+\frac{c^4 \left(6 a d^2+5 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{8 d^7}+\frac{b x^5 \sqrt{d x-c} \sqrt{c+d x}}{6 d^2}",1,"(c^2*(5*b*c^2 + 6*a*d^2)*x*Sqrt[-c + d*x]*Sqrt[c + d*x])/(16*d^6) + ((5*b*c^2 + 6*a*d^2)*x^3*Sqrt[-c + d*x]*Sqrt[c + d*x])/(24*d^4) + (b*x^5*Sqrt[-c + d*x]*Sqrt[c + d*x])/(6*d^2) + (c^4*(5*b*c^2 + 6*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/(8*d^7)","A",8,7,31,0.2258,1,"{460, 100, 12, 90, 63, 217, 206}"
359,1,118,0,0.0864362,"\int \frac{x^3 \left(a+b x^2\right)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(x^3*(a + b*x^2))/(Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{x^2 \sqrt{d x-c} \sqrt{c+d x} \left(5 a d^2+4 b c^2\right)}{15 d^4}+\frac{2 c^2 \sqrt{d x-c} \sqrt{c+d x} \left(5 a d^2+4 b c^2\right)}{15 d^6}+\frac{b x^4 \sqrt{d x-c} \sqrt{c+d x}}{5 d^2}","\frac{x^2 \sqrt{d x-c} \sqrt{c+d x} \left(5 a d^2+4 b c^2\right)}{15 d^4}+\frac{2 c^2 \sqrt{d x-c} \sqrt{c+d x} \left(5 a d^2+4 b c^2\right)}{15 d^6}+\frac{b x^4 \sqrt{d x-c} \sqrt{c+d x}}{5 d^2}",1,"(2*c^2*(4*b*c^2 + 5*a*d^2)*Sqrt[-c + d*x]*Sqrt[c + d*x])/(15*d^6) + ((4*b*c^2 + 5*a*d^2)*x^2*Sqrt[-c + d*x]*Sqrt[c + d*x])/(15*d^4) + (b*x^4*Sqrt[-c + d*x]*Sqrt[c + d*x])/(5*d^2)","A",4,4,31,0.1290,1,"{460, 100, 12, 74}"
360,1,118,0,0.096774,"\int \frac{x^2 \left(a+b x^2\right)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(x^2*(a + b*x^2))/(Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{x \sqrt{d x-c} \sqrt{c+d x} \left(4 a d^2+3 b c^2\right)}{8 d^4}+\frac{c^2 \left(4 a d^2+3 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{4 d^5}+\frac{b x^3 \sqrt{d x-c} \sqrt{c+d x}}{4 d^2}","\frac{x \sqrt{d x-c} \sqrt{c+d x} \left(4 a d^2+3 b c^2\right)}{8 d^4}+\frac{c^2 \left(4 a d^2+3 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{4 d^5}+\frac{b x^3 \sqrt{d x-c} \sqrt{c+d x}}{4 d^2}",1,"((3*b*c^2 + 4*a*d^2)*x*Sqrt[-c + d*x]*Sqrt[c + d*x])/(8*d^4) + (b*x^3*Sqrt[-c + d*x]*Sqrt[c + d*x])/(4*d^2) + (c^2*(3*b*c^2 + 4*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/(4*d^5)","A",6,6,31,0.1935,1,"{460, 90, 12, 63, 217, 206}"
361,1,72,0,0.0463676,"\int \frac{x \left(a+b x^2\right)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(x*(a + b*x^2))/(Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{\sqrt{d x-c} \sqrt{c+d x} \left(3 a d^2+2 b c^2\right)}{3 d^4}+\frac{b x^2 \sqrt{d x-c} \sqrt{c+d x}}{3 d^2}","\frac{\sqrt{d x-c} \sqrt{c+d x} \left(3 a d^2+2 b c^2\right)}{3 d^4}+\frac{b x^2 \sqrt{d x-c} \sqrt{c+d x}}{3 d^2}",1,"((2*b*c^2 + 3*a*d^2)*Sqrt[-c + d*x]*Sqrt[c + d*x])/(3*d^4) + (b*x^2*Sqrt[-c + d*x]*Sqrt[c + d*x])/(3*d^2)","A",2,2,29,0.06897,1,"{460, 74}"
362,1,68,0,0.0323963,"\int \frac{a+b x^2}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(a + b*x^2)/(Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{\left(2 a d^2+b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d^3}+\frac{b x \sqrt{d x-c} \sqrt{c+d x}}{2 d^2}","\frac{\left(2 a d^2+b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d^3}+\frac{b x \sqrt{d x-c} \sqrt{c+d x}}{2 d^2}",1,"(b*x*Sqrt[-c + d*x]*Sqrt[c + d*x])/(2*d^2) + ((b*c^2 + 2*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/d^3","A",4,4,28,0.1429,1,"{389, 63, 217, 206}"
363,1,56,0,0.0687923,"\int \frac{a+b x^2}{x \sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(a + b*x^2)/(x*Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{a \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{c}+\frac{b \sqrt{d x-c} \sqrt{c+d x}}{d^2}","\frac{a \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{c}+\frac{b \sqrt{d x-c} \sqrt{c+d x}}{d^2}",1,"(b*Sqrt[-c + d*x]*Sqrt[c + d*x])/d^2 + (a*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c])/c","A",3,3,31,0.09677,1,"{460, 92, 205}"
364,1,57,0,0.0747374,"\int \frac{a+b x^2}{x^2 \sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(a + b*x^2)/(x^2*Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{a \sqrt{d x-c} \sqrt{c+d x}}{c^2 x}+\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d}","\frac{a \sqrt{d x-c} \sqrt{c+d x}}{c^2 x}+\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d}",1,"(a*Sqrt[-c + d*x]*Sqrt[c + d*x])/(c^2*x) + (2*b*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/d","A",4,4,31,0.1290,1,"{454, 63, 217, 206}"
365,1,76,0,0.072997,"\int \frac{a+b x^2}{x^3 \sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(a + b*x^2)/(x^3*Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{\left(a d^2+2 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{2 c^3}+\frac{a \sqrt{d x-c} \sqrt{c+d x}}{2 c^2 x^2}","\frac{\left(a d^2+2 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{2 c^3}+\frac{a \sqrt{d x-c} \sqrt{c+d x}}{2 c^2 x^2}",1,"(a*Sqrt[-c + d*x]*Sqrt[c + d*x])/(2*c^2*x^2) + ((2*b*c^2 + a*d^2)*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c])/(2*c^3)","A",3,3,31,0.09677,1,"{454, 92, 205}"
366,1,75,0,0.0693193,"\int \frac{a+b x^2}{x^4 \sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(a + b*x^2)/(x^4*Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{\sqrt{d x-c} \sqrt{c+d x} \left(2 a d^2+3 b c^2\right)}{3 c^4 x}+\frac{a \sqrt{d x-c} \sqrt{c+d x}}{3 c^2 x^3}","\frac{\sqrt{d x-c} \sqrt{c+d x} \left(2 a d^2+3 b c^2\right)}{3 c^4 x}+\frac{a \sqrt{d x-c} \sqrt{c+d x}}{3 c^2 x^3}",1,"(a*Sqrt[-c + d*x]*Sqrt[c + d*x])/(3*c^2*x^3) + ((3*b*c^2 + 2*a*d^2)*Sqrt[-c + d*x]*Sqrt[c + d*x])/(3*c^4*x)","A",2,2,31,0.06452,1,"{454, 95}"
367,1,123,0,0.0953812,"\int \frac{a+b x^2}{x^5 \sqrt{-c+d x} \sqrt{c+d x}} \, dx","Int[(a + b*x^2)/(x^5*Sqrt[-c + d*x]*Sqrt[c + d*x]),x]","\frac{\sqrt{d x-c} \sqrt{c+d x} \left(3 a d^2+4 b c^2\right)}{8 c^4 x^2}+\frac{d^2 \left(3 a d^2+4 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{8 c^5}+\frac{a \sqrt{d x-c} \sqrt{c+d x}}{4 c^2 x^4}","\frac{\sqrt{d x-c} \sqrt{c+d x} \left(3 a d^2+4 b c^2\right)}{8 c^4 x^2}+\frac{d^2 \left(3 a d^2+4 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{8 c^5}+\frac{a \sqrt{d x-c} \sqrt{c+d x}}{4 c^2 x^4}",1,"(a*Sqrt[-c + d*x]*Sqrt[c + d*x])/(4*c^2*x^4) + ((4*b*c^2 + 3*a*d^2)*Sqrt[-c + d*x]*Sqrt[c + d*x])/(8*c^4*x^2) + (d^2*(4*b*c^2 + 3*a*d^2)*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c])/(8*c^5)","A",5,5,31,0.1613,1,"{454, 103, 12, 92, 205}"
368,1,161,0,0.1229362,"\int \frac{x^4 \left(a+b x^2\right)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(x^4*(a + b*x^2))/((-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{x^3 \left(4 a d^2+5 b c^2\right)}{4 d^4 \sqrt{d x-c} \sqrt{c+d x}}+\frac{3 x \sqrt{d x-c} \sqrt{c+d x} \left(4 a d^2+5 b c^2\right)}{8 d^6}+\frac{3 c^2 \left(4 a d^2+5 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{4 d^7}+\frac{b x^5}{4 d^2 \sqrt{d x-c} \sqrt{c+d x}}","-\frac{x^3 \left(4 a d^2+5 b c^2\right)}{4 d^4 \sqrt{d x-c} \sqrt{c+d x}}+\frac{3 x \sqrt{d x-c} \sqrt{c+d x} \left(4 a d^2+5 b c^2\right)}{8 d^6}+\frac{3 c^2 \left(4 a d^2+5 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{4 d^7}+\frac{b x^5}{4 d^2 \sqrt{d x-c} \sqrt{c+d x}}",1,"-((5*b*c^2 + 4*a*d^2)*x^3)/(4*d^4*Sqrt[-c + d*x]*Sqrt[c + d*x]) + (b*x^5)/(4*d^2*Sqrt[-c + d*x]*Sqrt[c + d*x]) + (3*(5*b*c^2 + 4*a*d^2)*x*Sqrt[-c + d*x]*Sqrt[c + d*x])/(8*d^6) + (3*c^2*(5*b*c^2 + 4*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/(4*d^7)","A",8,8,31,0.2581,1,"{460, 98, 21, 90, 12, 63, 217, 206}"
369,1,115,0,0.0943516,"\int \frac{x^3 \left(a+b x^2\right)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(x^3*(a + b*x^2))/((-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{x^2 \left(3 a d^2+4 b c^2\right)}{3 d^4 \sqrt{d x-c} \sqrt{c+d x}}+\frac{2 \sqrt{d x-c} \sqrt{c+d x} \left(3 a d^2+4 b c^2\right)}{3 d^6}+\frac{b x^4}{3 d^2 \sqrt{d x-c} \sqrt{c+d x}}","-\frac{x^2 \left(3 a d^2+4 b c^2\right)}{3 d^4 \sqrt{d x-c} \sqrt{c+d x}}+\frac{2 \sqrt{d x-c} \sqrt{c+d x} \left(3 a d^2+4 b c^2\right)}{3 d^6}+\frac{b x^4}{3 d^2 \sqrt{d x-c} \sqrt{c+d x}}",1,"-((4*b*c^2 + 3*a*d^2)*x^2)/(3*d^4*Sqrt[-c + d*x]*Sqrt[c + d*x]) + (b*x^4)/(3*d^2*Sqrt[-c + d*x]*Sqrt[c + d*x]) + (2*(4*b*c^2 + 3*a*d^2)*Sqrt[-c + d*x]*Sqrt[c + d*x])/(3*d^6)","A",4,4,31,0.1290,1,"{460, 98, 21, 74}"
370,1,152,0,0.1146804,"\int \frac{x^2 \left(a+b x^2\right)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(x^2*(a + b*x^2))/((-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{\sqrt{d x-c} \left(2 a d^2+3 b c^2\right)}{2 d^5 \sqrt{c+d x}}-\frac{c \left(2 a d^2+3 b c^2\right)}{2 d^5 \sqrt{d x-c} \sqrt{c+d x}}+\frac{\left(2 a d^2+3 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d^5}+\frac{b x^3}{2 d^2 \sqrt{d x-c} \sqrt{c+d x}}","-\frac{\sqrt{d x-c} \left(2 a d^2+3 b c^2\right)}{2 d^5 \sqrt{c+d x}}-\frac{c \left(2 a d^2+3 b c^2\right)}{2 d^5 \sqrt{d x-c} \sqrt{c+d x}}+\frac{\left(2 a d^2+3 b c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d^5}+\frac{b x^3}{2 d^2 \sqrt{d x-c} \sqrt{c+d x}}",1,"-(c*(3*b*c^2 + 2*a*d^2))/(2*d^5*Sqrt[-c + d*x]*Sqrt[c + d*x]) + (b*x^3)/(2*d^2*Sqrt[-c + d*x]*Sqrt[c + d*x]) - ((3*b*c^2 + 2*a*d^2)*Sqrt[-c + d*x])/(2*d^5*Sqrt[c + d*x]) + ((3*b*c^2 + 2*a*d^2)*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/d^5","A",7,7,31,0.2258,1,"{460, 89, 12, 78, 63, 217, 206}"
371,1,76,0,0.0535191,"\int \frac{x \left(a+b x^2\right)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(x*(a + b*x^2))/((-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{\sqrt{d x-c} \sqrt{c+d x} \left(a d^2+2 b c^2\right)}{c^2 d^4}-\frac{x^2 \left(\frac{a}{c^2}+\frac{b}{d^2}\right)}{\sqrt{d x-c} \sqrt{c+d x}}","\frac{\sqrt{d x-c} \sqrt{c+d x} \left(a d^2+2 b c^2\right)}{c^2 d^4}-\frac{x^2 \left(\frac{a}{c^2}+\frac{b}{d^2}\right)}{\sqrt{d x-c} \sqrt{c+d x}}",1,"-(((a/c^2 + b/d^2)*x^2)/(Sqrt[-c + d*x]*Sqrt[c + d*x])) + ((2*b*c^2 + a*d^2)*Sqrt[-c + d*x]*Sqrt[c + d*x])/(c^2*d^4)","A",2,2,29,0.06897,1,"{458, 74}"
372,1,63,0,0.0316689,"\int \frac{a+b x^2}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(a + b*x^2)/((-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d^3}-\frac{x \left(\frac{a}{c^2}+\frac{b}{d^2}\right)}{\sqrt{d x-c} \sqrt{c+d x}}","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{d x-c}}{\sqrt{c+d x}}\right)}{d^3}-\frac{x \left(\frac{a}{c^2}+\frac{b}{d^2}\right)}{\sqrt{d x-c} \sqrt{c+d x}}",1,"-(((a/c^2 + b/d^2)*x)/(Sqrt[-c + d*x]*Sqrt[c + d*x])) + (2*b*ArcTanh[Sqrt[-c + d*x]/Sqrt[c + d*x]])/d^3","A",4,4,28,0.1429,1,"{386, 63, 217, 206}"
373,1,65,0,0.0805375,"\int \frac{a+b x^2}{x (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(a + b*x^2)/(x*(-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{\frac{a}{c^2}+\frac{b}{d^2}}{\sqrt{d x-c} \sqrt{c+d x}}-\frac{a \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{c^3}","-\frac{\frac{a}{c^2}+\frac{b}{d^2}}{\sqrt{d x-c} \sqrt{c+d x}}-\frac{a \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{c^3}",1,"-((a/c^2 + b/d^2)/(Sqrt[-c + d*x]*Sqrt[c + d*x])) - (a*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c])/c^3","A",3,3,31,0.09677,1,"{458, 92, 205}"
374,1,67,0,0.076683,"\int \frac{a+b x^2}{x^2 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(a + b*x^2)/(x^2*(-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{a}{c^2 x \sqrt{d x-c} \sqrt{c+d x}}-\frac{x \left(2 a d^2+b c^2\right)}{c^4 \sqrt{d x-c} \sqrt{c+d x}}","\frac{a}{c^2 x \sqrt{d x-c} \sqrt{c+d x}}-\frac{x \left(2 a d^2+b c^2\right)}{c^4 \sqrt{d x-c} \sqrt{c+d x}}",1,"a/(c^2*x*Sqrt[-c + d*x]*Sqrt[c + d*x]) - ((b*c^2 + 2*a*d^2)*x)/(c^4*Sqrt[-c + d*x]*Sqrt[c + d*x])","A",2,2,31,0.06452,1,"{454, 39}"
375,1,117,0,0.0975361,"\int \frac{a+b x^2}{x^3 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(a + b*x^2)/(x^3*(-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{3 a d^2+2 b c^2}{2 c^4 \sqrt{d x-c} \sqrt{c+d x}}-\frac{\left(3 a d^2+2 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{2 c^5}+\frac{a}{2 c^2 x^2 \sqrt{d x-c} \sqrt{c+d x}}","-\frac{3 a d^2+2 b c^2}{2 c^4 \sqrt{d x-c} \sqrt{c+d x}}-\frac{\left(3 a d^2+2 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{2 c^5}+\frac{a}{2 c^2 x^2 \sqrt{d x-c} \sqrt{c+d x}}",1,"-(2*b*c^2 + 3*a*d^2)/(2*c^4*Sqrt[-c + d*x]*Sqrt[c + d*x]) + a/(2*c^2*x^2*Sqrt[-c + d*x]*Sqrt[c + d*x]) - ((2*b*c^2 + 3*a*d^2)*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c])/(2*c^5)","A",5,5,31,0.1613,1,"{454, 104, 21, 92, 205}"
376,1,119,0,0.0956436,"\int \frac{a+b x^2}{x^4 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(a + b*x^2)/(x^4*(-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{2 d^2 x \left(4 a d^2+3 b c^2\right)}{3 c^6 \sqrt{d x-c} \sqrt{c+d x}}+\frac{4 a d^2+3 b c^2}{3 c^4 x \sqrt{d x-c} \sqrt{c+d x}}+\frac{a}{3 c^2 x^3 \sqrt{d x-c} \sqrt{c+d x}}","-\frac{2 d^2 x \left(4 a d^2+3 b c^2\right)}{3 c^6 \sqrt{d x-c} \sqrt{c+d x}}+\frac{4 a d^2+3 b c^2}{3 c^4 x \sqrt{d x-c} \sqrt{c+d x}}+\frac{a}{3 c^2 x^3 \sqrt{d x-c} \sqrt{c+d x}}",1,"a/(3*c^2*x^3*Sqrt[-c + d*x]*Sqrt[c + d*x]) + (3*b*c^2 + 4*a*d^2)/(3*c^4*x*Sqrt[-c + d*x]*Sqrt[c + d*x]) - (2*d^2*(3*b*c^2 + 4*a*d^2)*x)/(3*c^6*Sqrt[-c + d*x]*Sqrt[c + d*x])","A",4,4,31,0.1290,1,"{454, 103, 12, 39}"
377,1,166,0,0.1202127,"\int \frac{a+b x^2}{x^5 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx","Int[(a + b*x^2)/(x^5*(-c + d*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{5 a d^2+4 b c^2}{8 c^4 x^2 \sqrt{d x-c} \sqrt{c+d x}}-\frac{3 d^2 \left(5 a d^2+4 b c^2\right)}{8 c^6 \sqrt{d x-c} \sqrt{c+d x}}-\frac{3 d^2 \left(5 a d^2+4 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{8 c^7}+\frac{a}{4 c^2 x^4 \sqrt{d x-c} \sqrt{c+d x}}","\frac{5 a d^2+4 b c^2}{8 c^4 x^2 \sqrt{d x-c} \sqrt{c+d x}}-\frac{3 d^2 \left(5 a d^2+4 b c^2\right)}{8 c^6 \sqrt{d x-c} \sqrt{c+d x}}-\frac{3 d^2 \left(5 a d^2+4 b c^2\right) \tan ^{-1}\left(\frac{\sqrt{d x-c} \sqrt{c+d x}}{c}\right)}{8 c^7}+\frac{a}{4 c^2 x^4 \sqrt{d x-c} \sqrt{c+d x}}",1,"(-3*d^2*(4*b*c^2 + 5*a*d^2))/(8*c^6*Sqrt[-c + d*x]*Sqrt[c + d*x]) + a/(4*c^2*x^4*Sqrt[-c + d*x]*Sqrt[c + d*x]) + (4*b*c^2 + 5*a*d^2)/(8*c^4*x^2*Sqrt[-c + d*x]*Sqrt[c + d*x]) - (3*d^2*(4*b*c^2 + 5*a*d^2)*ArcTan[(Sqrt[-c + d*x]*Sqrt[c + d*x])/c])/(8*c^7)","A",7,7,31,0.2258,1,"{454, 103, 12, 104, 21, 92, 205}"
378,1,40,0,0.0544183,"\int \frac{1+c^2 x^2}{x \sqrt{-1+c x} \sqrt{1+c x}} \, dx","Int[(1 + c^2*x^2)/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]),x]","\sqrt{c x-1} \sqrt{c x+1}+\tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)","\sqrt{c x-1} \sqrt{c x+1}+\tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)",1,"Sqrt[-1 + c*x]*Sqrt[1 + c*x] + ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]]","A",3,3,31,0.09677,1,"{460, 92, 205}"
379,1,53,0,0.0907204,"\int \frac{x^{-\frac{2 b^2 c+a^2 d}{b^2 c+a^2 d}} \left(c+d x^2\right)}{\sqrt{-a+b x} \sqrt{a+b x}} \, dx","Int[(c + d*x^2)/(x^((2*b^2*c + a^2*d)/(b^2*c + a^2*d))*Sqrt[-a + b*x]*Sqrt[a + b*x]),x]","\sqrt{b x-a} \sqrt{a+b x} \left(\frac{c}{a^2}+\frac{d}{b^2}\right) x^{-\frac{b^2 c}{a^2 d+b^2 c}}","\sqrt{b x-a} \sqrt{a+b x} \left(\frac{c}{a^2}+\frac{d}{b^2}\right) x^{-\frac{b^2 c}{a^2 d+b^2 c}}",1,"((c/a^2 + d/b^2)*Sqrt[-a + b*x]*Sqrt[a + b*x])/x^((b^2*c)/(b^2*c + a^2*d))","A",1,1,57,0.01754,1,"{450}"
380,1,36,0,0.0203589,"\int \frac{1}{\sqrt{-1-\sqrt{x}} \sqrt{-1+\sqrt{x}} \sqrt{1+x}} \, dx","Int[1/(Sqrt[-1 - Sqrt[x]]*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + x]),x]","\frac{\sqrt{1-x} \sin ^{-1}(x)}{\sqrt{-\sqrt{x}-1} \sqrt{\sqrt{x}-1}}","\frac{\sqrt{1-x} \sin ^{-1}(x)}{\sqrt{-\sqrt{x}-1} \sqrt{\sqrt{x}-1}}",1,"(Sqrt[1 - x]*ArcSin[x])/(Sqrt[-1 - Sqrt[x]]*Sqrt[-1 + Sqrt[x]])","A",3,3,32,0.09375,1,"{519, 41, 216}"
381,1,75,0,0.0502034,"\int \frac{1}{\sqrt{a-b \sqrt{x}} \sqrt{a+b \sqrt{x}} \sqrt{a^2+b^2 x}} \, dx","Int[1/(Sqrt[a - b*Sqrt[x]]*Sqrt[a + b*Sqrt[x]]*Sqrt[a^2 + b^2*x]),x]","-\frac{2 \sqrt{a^2-b^2 x} \tan ^{-1}\left(\frac{\sqrt{a^2-b^2 x}}{\sqrt{a^2+b^2 x}}\right)}{b^2 \sqrt{a-b \sqrt{x}} \sqrt{a+b \sqrt{x}}}","-\frac{2 \sqrt{a^2-b^2 x} \tan ^{-1}\left(\frac{\sqrt{a^2-b^2 x}}{\sqrt{a^2+b^2 x}}\right)}{b^2 \sqrt{a-b \sqrt{x}} \sqrt{a+b \sqrt{x}}}",1,"(-2*Sqrt[a^2 - b^2*x]*ArcTan[Sqrt[a^2 - b^2*x]/Sqrt[a^2 + b^2*x]])/(b^2*Sqrt[a - b*Sqrt[x]]*Sqrt[a + b*Sqrt[x]])","A",4,4,41,0.09756,1,"{519, 63, 217, 203}"
382,1,113,0,0.0904555,"\int \left(a-b x^n\right)^p \left(a+b x^n\right)^p \left(c+d x^{2 n}\right)^q \, dx","Int[(a - b*x^n)^p*(a + b*x^n)^p*(c + d*x^(2*n))^q,x]","x \left(a-b x^n\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \left(c+d x^{2 n}\right)^q \left(\frac{d x^{2 n}}{c}+1\right)^{-q} F_1\left(\frac{1}{2 n};-p,-q;\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2},-\frac{d x^{2 n}}{c}\right)","x \left(a-b x^n\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \left(c+d x^{2 n}\right)^q \left(\frac{d x^{2 n}}{c}+1\right)^{-q} F_1\left(\frac{1}{2 n};-p,-q;\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2},-\frac{d x^{2 n}}{c}\right)",1,"(x*(a - b*x^n)^p*(a + b*x^n)^p*(c + d*x^(2*n))^q*AppellF1[1/(2*n), -p, -q, (2 + n^(-1))/2, (b^2*x^(2*n))/a^2, -((d*x^(2*n))/c)])/((1 - (b^2*x^(2*n))/a^2)^p*(1 + (d*x^(2*n))/c)^q)","A",4,3,31,0.09677,1,"{519, 430, 429}"
383,1,87,0,0.0587613,"\int \left(a-b x^n\right)^p \left(a+b x^n\right)^p \left(a^2+b^2 x^{2 n}\right)^p \, dx","Int[(a - b*x^n)^p*(a + b*x^n)^p*(a^2 + b^2*x^(2*n))^p,x]","x \left(a-b x^n\right)^p \left(a+b x^n\right)^p \left(a^2+b^2 x^{2 n}\right)^p \left(1-\frac{b^4 x^{4 n}}{a^4}\right)^{-p} \, _2F_1\left(\frac{1}{4 n},-p;\frac{1}{4} \left(4+\frac{1}{n}\right);\frac{b^4 x^{4 n}}{a^4}\right)","x \left(a-b x^n\right)^p \left(a+b x^n\right)^p \left(a^2+b^2 x^{2 n}\right)^p \left(1-\frac{b^4 x^{4 n}}{a^4}\right)^{-p} \, _2F_1\left(\frac{1}{4 n},-p;\frac{1}{4} \left(4+\frac{1}{n}\right);\frac{b^4 x^{4 n}}{a^4}\right)",1,"(x*(a - b*x^n)^p*(a + b*x^n)^p*(a^2 + b^2*x^(2*n))^p*Hypergeometric2F1[1/(4*n), -p, (4 + n^(-1))/4, (b^4*x^(4*n))/a^4])/(1 - (b^4*x^(4*n))/a^4)^p","A",4,4,35,0.1143,1,"{519, 253, 246, 245}"
384,1,76,0,0.056669,"\int \frac{\left(c+d x^{2 n}\right)^p}{\left(a-b x^n\right) \left(a+b x^n\right)} \, dx","Int[(c + d*x^(2*n))^p/((a - b*x^n)*(a + b*x^n)),x]","\frac{x \left(c+d x^{2 n}\right)^p \left(\frac{d x^{2 n}}{c}+1\right)^{-p} F_1\left(\frac{1}{2 n};1,-p;\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2},-\frac{d x^{2 n}}{c}\right)}{a^2}","\frac{x \left(c+d x^{2 n}\right)^p \left(\frac{d x^{2 n}}{c}+1\right)^{-p} F_1\left(\frac{1}{2 n};1,-p;\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2},-\frac{d x^{2 n}}{c}\right)}{a^2}",1,"(x*(c + d*x^(2*n))^p*AppellF1[1/(2*n), 1, -p, (2 + n^(-1))/2, (b^2*x^(2*n))/a^2, -((d*x^(2*n))/c)])/(a^2*(1 + (d*x^(2*n))/c)^p)","A",3,3,31,0.09677,1,"{517, 430, 429}"
385,1,104,0,0.1223899,"\int \left(a-b x^{n/2}\right)^p \left(a+b x^{n/2}\right)^p \left(\frac{a^2 d (1+p)}{b^2 \left(1+\frac{-1-2 n-n p}{n}\right)}+d x^n\right)^{\frac{-1-2 n-n p}{n}} \, dx","Int[(a - b*x^(n/2))^p*(a + b*x^(n/2))^p*((a^2*d*(1 + p))/(b^2*(1 + (-1 - 2*n - n*p)/n)) + d*x^n)^((-1 - 2*n - n*p)/n),x]","-\frac{b^2 x (n p+n+1) \left(a^2-b^2 x^n\right) \left(a-b x^{n/2}\right)^p \left(a+b x^{n/2}\right)^p \left(d x^n-\frac{a^2 d n (p+1)}{b^2 (n p+n+1)}\right)^{-\frac{n p+n+1}{n}}}{a^4 d n (p+1)}","-\frac{b^2 x (n p+n+1) \left(a-b x^{n/2}\right)^{p+1} \left(a+b x^{n/2}\right)^{p+1} \left(d x^n-\frac{a^2 d n (p+1)}{b^2 (n p+n+1)}\right)^{-\frac{n p+n+1}{n}}}{a^4 d n (p+1)}",1,"-((b^2*(1 + n + n*p)*x*(a - b*x^(n/2))^p*(a + b*x^(n/2))^p*(a^2 - b^2*x^n))/(a^4*d*n*(1 + p)*(-((a^2*d*n*(1 + p))/(b^2*(1 + n + n*p))) + d*x^n)^((1 + n + n*p)/n)))","A",2,2,76,0.02632,1,"{519, 381}"