1,1,163,0,0.1851707,"\int \left(d+e x^3\right)^5 \left(a+b x^3+c x^6\right) \, dx","Int[(d + e*x^3)^5*(a + b*x^3 + c*x^6),x]","\frac{1}{16} e^3 x^{16} \left(e (a e+5 b d)+10 c d^2\right)+\frac{5}{13} d e^2 x^{13} \left(e (a e+2 b d)+2 c d^2\right)+\frac{1}{2} d^2 e x^{10} \left(2 e (a e+b d)+c d^2\right)+\frac{1}{7} d^3 x^7 \left(5 e (2 a e+b d)+c d^2\right)+\frac{1}{4} d^4 x^4 (5 a e+b d)+a d^5 x+\frac{1}{19} e^4 x^{19} (b e+5 c d)+\frac{1}{22} c e^5 x^{22}","\frac{1}{16} e^3 x^{16} \left(e (a e+5 b d)+10 c d^2\right)+\frac{5}{13} d e^2 x^{13} \left(e (a e+2 b d)+2 c d^2\right)+\frac{1}{2} d^2 e x^{10} \left(2 e (a e+b d)+c d^2\right)+\frac{1}{7} d^3 x^7 \left(5 e (2 a e+b d)+c d^2\right)+\frac{1}{4} d^4 x^4 (5 a e+b d)+a d^5 x+\frac{1}{19} e^4 x^{19} (b e+5 c d)+\frac{1}{22} c e^5 x^{22}",1,"a*d^5*x + (d^4*(b*d + 5*a*e)*x^4)/4 + (d^3*(c*d^2 + 5*e*(b*d + 2*a*e))*x^7)/7 + (d^2*e*(c*d^2 + 2*e*(b*d + a*e))*x^10)/2 + (5*d*e^2*(2*c*d^2 + e*(2*b*d + a*e))*x^13)/13 + (e^3*(10*c*d^2 + e*(5*b*d + a*e))*x^16)/16 + (e^4*(5*c*d + b*e)*x^19)/19 + (c*e^5*x^22)/22","A",2,1,22,0.04545,1,"{1407}"
2,1,135,0,0.125073,"\int \left(d+e x^3\right)^4 \left(a+b x^3+c x^6\right) \, dx","Int[(d + e*x^3)^4*(a + b*x^3 + c*x^6),x]","\frac{1}{13} e^2 x^{13} \left(e (a e+4 b d)+6 c d^2\right)+\frac{1}{7} d^2 x^7 \left(6 a e^2+4 b d e+c d^2\right)+\frac{1}{5} d e x^{10} \left(e (2 a e+3 b d)+2 c d^2\right)+\frac{1}{4} d^3 x^4 (4 a e+b d)+a d^4 x+\frac{1}{16} e^3 x^{16} (b e+4 c d)+\frac{1}{19} c e^4 x^{19}","\frac{1}{13} e^2 x^{13} \left(e (a e+4 b d)+6 c d^2\right)+\frac{1}{7} d^2 x^7 \left(6 a e^2+4 b d e+c d^2\right)+\frac{1}{5} d e x^{10} \left(e (2 a e+3 b d)+2 c d^2\right)+\frac{1}{4} d^3 x^4 (4 a e+b d)+a d^4 x+\frac{1}{16} e^3 x^{16} (b e+4 c d)+\frac{1}{19} c e^4 x^{19}",1,"a*d^4*x + (d^3*(b*d + 4*a*e)*x^4)/4 + (d^2*(c*d^2 + 4*b*d*e + 6*a*e^2)*x^7)/7 + (d*e*(2*c*d^2 + e*(3*b*d + 2*a*e))*x^10)/5 + (e^2*(6*c*d^2 + e*(4*b*d + a*e))*x^13)/13 + (e^3*(4*c*d + b*e)*x^16)/16 + (c*e^4*x^19)/19","A",2,1,22,0.04545,1,"{1407}"
3,1,103,0,0.0969754,"\int \left(d+e x^3\right)^3 \left(a+b x^3+c x^6\right) \, dx","Int[(d + e*x^3)^3*(a + b*x^3 + c*x^6),x]","\frac{1}{10} e x^{10} \left(e (a e+3 b d)+3 c d^2\right)+\frac{1}{7} d x^7 \left(3 e (a e+b d)+c d^2\right)+\frac{1}{4} d^2 x^4 (3 a e+b d)+a d^3 x+\frac{1}{13} e^2 x^{13} (b e+3 c d)+\frac{1}{16} c e^3 x^{16}","\frac{1}{10} e x^{10} \left(e (a e+3 b d)+3 c d^2\right)+\frac{1}{7} d x^7 \left(3 e (a e+b d)+c d^2\right)+\frac{1}{4} d^2 x^4 (3 a e+b d)+a d^3 x+\frac{1}{13} e^2 x^{13} (b e+3 c d)+\frac{1}{16} c e^3 x^{16}",1,"a*d^3*x + (d^2*(b*d + 3*a*e)*x^4)/4 + (d*(c*d^2 + 3*e*(b*d + a*e))*x^7)/7 + (e*(3*c*d^2 + e*(3*b*d + a*e))*x^10)/10 + (e^2*(3*c*d + b*e)*x^13)/13 + (c*e^3*x^16)/16","A",2,1,22,0.04545,1,"{1407}"
4,1,73,0,0.0622015,"\int \left(d+e x^3\right)^2 \left(a+b x^3+c x^6\right) \, dx","Int[(d + e*x^3)^2*(a + b*x^3 + c*x^6),x]","\frac{1}{7} x^7 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{4} d x^4 (2 a e+b d)+a d^2 x+\frac{1}{10} e x^{10} (b e+2 c d)+\frac{1}{13} c e^2 x^{13}","\frac{1}{7} x^7 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{4} d x^4 (2 a e+b d)+a d^2 x+\frac{1}{10} e x^{10} (b e+2 c d)+\frac{1}{13} c e^2 x^{13}",1,"a*d^2*x + (d*(b*d + 2*a*e)*x^4)/4 + ((c*d^2 + e*(2*b*d + a*e))*x^7)/7 + (e*(2*c*d + b*e)*x^10)/10 + (c*e^2*x^13)/13","A",2,1,22,0.04545,1,"{1407}"
5,1,42,0,0.0278242,"\int \left(d+e x^3\right) \left(a+b x^3+c x^6\right) \, dx","Int[(d + e*x^3)*(a + b*x^3 + c*x^6),x]","\frac{1}{4} x^4 (a e+b d)+a d x+\frac{1}{7} x^7 (b e+c d)+\frac{1}{10} c e x^{10}","\frac{1}{4} x^4 (a e+b d)+a d x+\frac{1}{7} x^7 (b e+c d)+\frac{1}{10} c e x^{10}",1,"a*d*x + ((b*d + a*e)*x^4)/4 + ((c*d + b*e)*x^7)/7 + (c*e*x^10)/10","A",2,1,20,0.05000,1,"{1407}"
6,1,188,0,0.2111148,"\int \frac{a+b x^3+c x^6}{d+e x^3} \, dx","Int[(a + b*x^3 + c*x^6)/(d + e*x^3),x]","-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(a e^2-b d e+c d^2\right)}{6 d^{2/3} e^{7/3}}+\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(a e^2-b d e+c d^2\right)}{3 d^{2/3} e^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(a e^2-b d e+c d^2\right)}{\sqrt{3} d^{2/3} e^{7/3}}-\frac{x (c d-b e)}{e^2}+\frac{c x^4}{4 e}","-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(a e^2-b d e+c d^2\right)}{6 d^{2/3} e^{7/3}}+\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(a e^2-b d e+c d^2\right)}{3 d^{2/3} e^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(a e^2-b d e+c d^2\right)}{\sqrt{3} d^{2/3} e^{7/3}}-\frac{x (c d-b e)}{e^2}+\frac{c x^4}{4 e}",1,"-(((c*d - b*e)*x)/e^2) + (c*x^4)/(4*e) - ((c*d^2 - b*d*e + a*e^2)*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*d^(2/3)*e^(7/3)) + ((c*d^2 - b*d*e + a*e^2)*Log[d^(1/3) + e^(1/3)*x])/(3*d^(2/3)*e^(7/3)) - ((c*d^2 - b*d*e + a*e^2)*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(6*d^(2/3)*e^(7/3))","A",8,8,22,0.3636,1,"{1411, 388, 200, 31, 634, 617, 204, 628}"
7,1,213,0,0.225653,"\int \frac{a+b x^3+c x^6}{\left(d+e x^3\right)^2} \, dx","Int[(a + b*x^3 + c*x^6)/(d + e*x^3)^2,x]","\frac{x \left(a e^2-b d e+c d^2\right)}{3 d e^2 \left(d+e x^3\right)}+\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(4 c d^2-e (2 a e+b d)\right)}{18 d^{5/3} e^{7/3}}-\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(4 c d^2-e (2 a e+b d)\right)}{9 d^{5/3} e^{7/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(4 c d^2-e (2 a e+b d)\right)}{3 \sqrt{3} d^{5/3} e^{7/3}}+\frac{c x}{e^2}","\frac{x \left(a e^2-b d e+c d^2\right)}{3 d e^2 \left(d+e x^3\right)}+\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(4 c d^2-e (2 a e+b d)\right)}{18 d^{5/3} e^{7/3}}-\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(4 c d^2-e (2 a e+b d)\right)}{9 d^{5/3} e^{7/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(4 c d^2-e (2 a e+b d)\right)}{3 \sqrt{3} d^{5/3} e^{7/3}}+\frac{c x}{e^2}",1,"(c*x)/e^2 + ((c*d^2 - b*d*e + a*e^2)*x)/(3*d*e^2*(d + e*x^3)) + ((4*c*d^2 - e*(b*d + 2*a*e))*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(3*Sqrt[3]*d^(5/3)*e^(7/3)) - ((4*c*d^2 - e*(b*d + 2*a*e))*Log[d^(1/3) + e^(1/3)*x])/(9*d^(5/3)*e^(7/3)) + ((4*c*d^2 - e*(b*d + 2*a*e))*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(18*d^(5/3)*e^(7/3))","A",8,8,22,0.3636,1,"{1409, 388, 200, 31, 634, 617, 204, 628}"
8,1,242,0,0.2624458,"\int \frac{a+b x^3+c x^6}{\left(d+e x^3\right)^3} \, dx","Int[(a + b*x^3 + c*x^6)/(d + e*x^3)^3,x]","-\frac{x \left(7 c d^2-e (5 a e+b d)\right)}{18 d^2 e^2 \left(d+e x^3\right)}+\frac{x \left(a e^2-b d e+c d^2\right)}{6 d e^2 \left(d+e x^3\right)^2}-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(e (5 a e+b d)+2 c d^2\right)}{54 d^{8/3} e^{7/3}}+\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(e (5 a e+b d)+2 c d^2\right)}{27 d^{8/3} e^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(e (5 a e+b d)+2 c d^2\right)}{9 \sqrt{3} d^{8/3} e^{7/3}}","-\frac{x \left(7 c d^2-e (5 a e+b d)\right)}{18 d^2 e^2 \left(d+e x^3\right)}+\frac{x \left(a e^2-b d e+c d^2\right)}{6 d e^2 \left(d+e x^3\right)^2}-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(e (5 a e+b d)+2 c d^2\right)}{54 d^{8/3} e^{7/3}}+\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(e (5 a e+b d)+2 c d^2\right)}{27 d^{8/3} e^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(e (5 a e+b d)+2 c d^2\right)}{9 \sqrt{3} d^{8/3} e^{7/3}}",1,"((c*d^2 - b*d*e + a*e^2)*x)/(6*d*e^2*(d + e*x^3)^2) - ((7*c*d^2 - e*(b*d + 5*a*e))*x)/(18*d^2*e^2*(d + e*x^3)) - ((2*c*d^2 + e*(b*d + 5*a*e))*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(9*Sqrt[3]*d^(8/3)*e^(7/3)) + ((2*c*d^2 + e*(b*d + 5*a*e))*Log[d^(1/3) + e^(1/3)*x])/(27*d^(8/3)*e^(7/3)) - ((2*c*d^2 + e*(b*d + 5*a*e))*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(54*d^(8/3)*e^(7/3))","A",8,8,22,0.3636,1,"{1409, 385, 200, 31, 634, 617, 204, 628}"
9,1,132,0,0.2179828,"\int \frac{x^8 \left(d+e x^3\right)}{a+b x^3+c x^6} \, dx","Int[(x^8*(d + e*x^3))/(a + b*x^3 + c*x^6),x]","-\frac{\left(a c e+b^2 (-e)+b c d\right) \log \left(a+b x^3+c x^6\right)}{6 c^3}-\frac{\left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c^3 \sqrt{b^2-4 a c}}+\frac{x^3 (c d-b e)}{3 c^2}+\frac{e x^6}{6 c}","-\frac{\left(a c e+b^2 (-e)+b c d\right) \log \left(a+b x^3+c x^6\right)}{6 c^3}-\frac{\left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c^3 \sqrt{b^2-4 a c}}+\frac{x^3 (c d-b e)}{3 c^2}+\frac{e x^6}{6 c}",1,"((c*d - b*e)*x^3)/(3*c^2) + (e*x^6)/(6*c) - ((b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*c^3*Sqrt[b^2 - 4*a*c]) - ((b*c*d - b^2*e + a*c*e)*Log[a + b*x^3 + c*x^6])/(6*c^3)","A",7,6,25,0.2400,1,"{1474, 800, 634, 618, 206, 628}"
10,1,97,0,0.119684,"\int \frac{x^5 \left(d+e x^3\right)}{a+b x^3+c x^6} \, dx","Int[(x^5*(d + e*x^3))/(a + b*x^3 + c*x^6),x]","\frac{\left(2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c^2 \sqrt{b^2-4 a c}}+\frac{(c d-b e) \log \left(a+b x^3+c x^6\right)}{6 c^2}+\frac{e x^3}{3 c}","\frac{\left(2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c^2 \sqrt{b^2-4 a c}}+\frac{(c d-b e) \log \left(a+b x^3+c x^6\right)}{6 c^2}+\frac{e x^3}{3 c}",1,"(e*x^3)/(3*c) + ((b*c*d - b^2*e + 2*a*c*e)*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*c^2*Sqrt[b^2 - 4*a*c]) + ((c*d - b*e)*Log[a + b*x^3 + c*x^6])/(6*c^2)","A",6,6,25,0.2400,1,"{1474, 773, 634, 618, 206, 628}"
11,1,72,0,0.0731691,"\int \frac{x^2 \left(d+e x^3\right)}{a+b x^3+c x^6} \, dx","Int[(x^2*(d + e*x^3))/(a + b*x^3 + c*x^6),x]","\frac{e \log \left(a+b x^3+c x^6\right)}{6 c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c \sqrt{b^2-4 a c}}","\frac{e \log \left(a+b x^3+c x^6\right)}{6 c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c \sqrt{b^2-4 a c}}",1,"-((2*c*d - b*e)*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*c*Sqrt[b^2 - 4*a*c]) + (e*Log[a + b*x^3 + c*x^6])/(6*c)","A",5,5,25,0.2000,1,"{1468, 634, 618, 206, 628}"
12,1,78,0,0.1279525,"\int \frac{d+e x^3}{x \left(a+b x^3+c x^6\right)} \, dx","Int[(d + e*x^3)/(x*(a + b*x^3 + c*x^6)),x]","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 a \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b x^3+c x^6\right)}{6 a}+\frac{d \log (x)}{a}","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 a \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b x^3+c x^6\right)}{6 a}+\frac{d \log (x)}{a}",1,"((b*d - 2*a*e)*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*a*Sqrt[b^2 - 4*a*c]) + (d*Log[x])/a - (d*Log[a + b*x^3 + c*x^6])/(6*a)","A",7,6,25,0.2400,1,"{1474, 800, 634, 618, 206, 628}"
13,1,112,0,0.1974859,"\int \frac{d+e x^3}{x^4 \left(a+b x^3+c x^6\right)} \, dx","Int[(d + e*x^3)/(x^4*(a + b*x^3 + c*x^6)),x]","-\frac{\left(-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 a^2 \sqrt{b^2-4 a c}}+\frac{(b d-a e) \log \left(a+b x^3+c x^6\right)}{6 a^2}-\frac{\log (x) (b d-a e)}{a^2}-\frac{d}{3 a x^3}","-\frac{\left(-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 a^2 \sqrt{b^2-4 a c}}+\frac{(b d-a e) \log \left(a+b x^3+c x^6\right)}{6 a^2}-\frac{\log (x) (b d-a e)}{a^2}-\frac{d}{3 a x^3}",1,"-d/(3*a*x^3) - ((b^2*d - 2*a*c*d - a*b*e)*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*a^2*Sqrt[b^2 - 4*a*c]) - ((b*d - a*e)*Log[x])/a^2 + ((b*d - a*e)*Log[a + b*x^3 + c*x^6])/(6*a^2)","A",7,6,25,0.2400,1,"{1474, 800, 634, 618, 206, 628}"
14,1,723,0,1.8132813,"\int \frac{x^4 \left(d+e x^3\right)}{a+b x^3+c x^6} \, dx","Int[(x^4*(d + e*x^3))/(a + b*x^3 + c*x^6),x]","\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{e x^2}{2 c}","\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{e x^2}{2 c}",1,"(e*x^2)/(2*c) - ((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*c^(5/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)) - ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*c^(5/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)) - ((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*c^(5/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)) - ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*c^(5/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)) + ((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*c^(5/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*c^(5/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3))","A",14,8,25,0.3200,1,"{1502, 1510, 292, 31, 634, 617, 204, 628}"
15,1,718,0,1.457421,"\int \frac{x^3 \left(d+e x^3\right)}{a+b x^3+c x^6} \, dx","Int[(x^3*(d + e*x^3))/(a + b*x^3 + c*x^6),x]","-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{e x}{c}","-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{e x}{c}",1,"(e*x)/c - ((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) - ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)) + ((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)) - ((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) - ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3))","A",14,8,25,0.3200,1,"{1502, 1422, 200, 31, 634, 617, 204, 628}"
16,1,634,0,0.7277491,"\int \frac{x \left(d+e x^3\right)}{a+b x^3+c x^6} \, dx","Int[(x*(d + e*x^3))/(a + b*x^3 + c*x^6),x]","\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{2/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{2/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{2/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{2/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{2/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{2/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}","\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{2/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{2/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{2/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{2/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{2/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{2/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}",1,"-(((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*c^(2/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3))) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*c^(2/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*c^(2/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*c^(2/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)) + ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*c^(2/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*c^(2/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3))","A",13,7,23,0.3043,1,"{1510, 292, 31, 634, 617, 204, 628}"
17,1,634,0,0.6537549,"\int \frac{d+e x^3}{a+b x^3+c x^6} \, dx","Int[(d + e*x^3)/(a + b*x^3 + c*x^6),x]","-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} \sqrt[3]{c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} \sqrt[3]{c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} \sqrt[3]{c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} \sqrt[3]{c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}","-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} \sqrt[3]{c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} \sqrt[3]{c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} \sqrt[3]{c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} \sqrt[3]{c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}",1,"-(((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3))) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)) + ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3))","A",13,7,22,0.3182,1,"{1422, 200, 31, 634, 617, 204, 628}"
18,1,653,0,1.1752591,"\int \frac{d+e x^3}{x^2 \left(a+b x^3+c x^6\right)} \, dx","Int[(d + e*x^3)/(x^2*(a + b*x^3 + c*x^6)),x]","-\frac{\sqrt[3]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt[3]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt[3]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt[3]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{d}{a x}","-\frac{\sqrt[3]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt[3]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt[3]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt[3]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{d}{a x}",1,"-(d/(a*x)) + (c^(1/3)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*a*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + (c^(1/3)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*a*(b + Sqrt[b^2 - 4*a*c])^(1/3)) + (c^(1/3)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*a*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + (c^(1/3)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*a*(b + Sqrt[b^2 - 4*a*c])^(1/3)) - (c^(1/3)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*a*(b - Sqrt[b^2 - 4*a*c])^(1/3)) - (c^(1/3)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*a*(b + Sqrt[b^2 - 4*a*c])^(1/3))","A",14,8,25,0.3200,1,"{1504, 1510, 292, 31, 634, 617, 204, 628}"
19,1,655,0,1.1100542,"\int \frac{d+e x^3}{x^3 \left(a+b x^3+c x^6\right)} \, dx","Int[(d + e*x^3)/(x^3*(a + b*x^3 + c*x^6)),x]","\frac{c^{2/3} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{c^{2/3} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{c^{2/3} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{c^{2/3} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{d}{2 a x^2}","\frac{c^{2/3} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{c^{2/3} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{c^{2/3} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{c^{2/3} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{d}{2 a x^2}",1,"-d/(2*a*x^2) + (c^(2/3)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*a*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + (c^(2/3)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*a*(b + Sqrt[b^2 - 4*a*c])^(2/3)) - (c^(2/3)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*a*(b - Sqrt[b^2 - 4*a*c])^(2/3)) - (c^(2/3)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*a*(b + Sqrt[b^2 - 4*a*c])^(2/3)) + (c^(2/3)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*a*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + (c^(2/3)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*a*(b + Sqrt[b^2 - 4*a*c])^(2/3))","A",14,8,25,0.3200,1,"{1504, 1422, 200, 31, 634, 617, 204, 628}"
20,1,46,0,0.0578566,"\int \frac{x^8 \left(1-x^3\right)}{1-x^3+x^6} \, dx","Int[(x^8*(1 - x^3))/(1 - x^3 + x^6),x]","-\frac{x^6}{6}+\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{x^6}{6}+\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-x^6/6 - ArcTan[(1 - 2*x^3)/Sqrt[3]]/(3*Sqrt[3]) + Log[1 - x^3 + x^6]/6","A",7,6,23,0.2609,1,"{1474, 800, 634, 618, 204, 628}"
21,1,31,0,0.0354362,"\int \frac{x^5 \left(1-x^3\right)}{1-x^3+x^6} \, dx","Int[(x^5*(1 - x^3))/(1 - x^3 + x^6),x]","-\frac{x^3}{3}-\frac{2 \tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{x^3}{3}-\frac{2 \tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-x^3/3 - (2*ArcTan[(1 - 2*x^3)/Sqrt[3]])/(3*Sqrt[3])","A",4,4,23,0.1739,1,"{1474, 773, 618, 204}"
22,1,39,0,0.0395079,"\int \frac{x^2 \left(1-x^3\right)}{1-x^3+x^6} \, dx","Int[(x^2*(1 - x^3))/(1 - x^3 + x^6),x]","-\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^3)/Sqrt[3]]/(3*Sqrt[3]) - Log[1 - x^3 + x^6]/6","A",5,5,23,0.2174,1,"{1468, 634, 618, 204, 628}"
23,1,41,0,0.05475,"\int \frac{1-x^3}{x \left(1-x^3+x^6\right)} \, dx","Int[(1 - x^3)/(x*(1 - x^3 + x^6)),x]","-\frac{1}{6} \log \left(x^6-x^3+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}+\log (x)","-\frac{1}{6} \log \left(x^6-x^3+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}+\log (x)",1,"ArcTan[(1 - 2*x^3)/Sqrt[3]]/(3*Sqrt[3]) + Log[x] - Log[1 - x^3 + x^6]/6","A",7,6,23,0.2609,1,"{1474, 800, 634, 618, 204, 628}"
24,1,31,0,0.0451354,"\int \frac{1-x^3}{x^4 \left(1-x^3+x^6\right)} \, dx","Int[(1 - x^3)/(x^4*(1 - x^3 + x^6)),x]","\frac{2 \tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{1}{3 x^3}","\frac{2 \tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{1}{3 x^3}",1,"-1/(3*x^3) + (2*ArcTan[(1 - 2*x^3)/Sqrt[3]])/(3*Sqrt[3])","A",5,4,23,0.1739,1,"{1474, 800, 618, 204}"
25,1,418,0,0.5375656,"\int \frac{x^6 \left(1-x^3\right)}{1-x^3+x^6} \, dx","Int[(x^6*(1 - x^3))/(1 - x^3 + x^6),x]","-\frac{x^4}{4}-\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}","-\frac{x^4}{4}-\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}",1,"-x^4/4 - ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) + ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) - ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) - ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 + I*Sqrt[3])^(2/3))","A",15,9,23,0.3913,1,"{1502, 12, 1374, 200, 31, 634, 617, 204, 628}"
26,1,382,0,0.327587,"\int \frac{x^4 \left(1-x^3\right)}{1-x^3+x^6} \, dx","Int[(x^4*(1 - x^3))/(1 - x^3 + x^6),x]","-\frac{x^2}{2}-\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1-i \sqrt{3}}}+\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1+i \sqrt{3}}}+\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}-\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}+\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}","-\frac{x^2}{2}-\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1-i \sqrt{3}}}+\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1+i \sqrt{3}}}+\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}-\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}+\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}",1,"-x^2/2 + ((I/3)*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/((1 - I*Sqrt[3])/2)^(1/3) - ((I/3)*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/((1 + I*Sqrt[3])/2)^(1/3) + ((I/3)*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(Sqrt[3]*((1 - I*Sqrt[3])/2)^(1/3)) - ((I/3)*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(Sqrt[3]*((1 + I*Sqrt[3])/2)^(1/3)) - ((I/3)*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(2^(2/3)*Sqrt[3]*(1 - I*Sqrt[3])^(1/3)) + ((I/3)*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(2^(2/3)*Sqrt[3]*(1 + I*Sqrt[3])^(1/3))","A",15,9,23,0.3913,1,"{1502, 12, 1375, 292, 31, 634, 617, 204, 628}"
27,1,378,0,0.25865,"\int \frac{x^3 \left(1-x^3\right)}{1-x^3+x^6} \, dx","Int[(x^3*(1 - x^3))/(1 - x^3 + x^6),x]","-\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{3} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{3} \left(1+i \sqrt{3}\right)^{2/3}}-x+\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{3 \sqrt{3} \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{2/3}}-\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{3 \sqrt{3} \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{2/3}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{2/3}}+\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{2/3}}","-\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{3} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{3} \left(1+i \sqrt{3}\right)^{2/3}}-x+\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{3 \sqrt{3} \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{2/3}}-\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{3 \sqrt{3} \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{2/3}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{2/3}}+\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{2/3}}",1,"-x - ((I/3)*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/((1 - I*Sqrt[3])/2)^(2/3) + ((I/3)*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/((1 + I*Sqrt[3])/2)^(2/3) + ((I/3)*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(Sqrt[3]*((1 - I*Sqrt[3])/2)^(2/3)) - ((I/3)*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(Sqrt[3]*((1 + I*Sqrt[3])/2)^(2/3)) - ((I/3)*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(2^(1/3)*Sqrt[3]*(1 - I*Sqrt[3])^(2/3)) + ((I/3)*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(2^(1/3)*Sqrt[3]*(1 + I*Sqrt[3])^(2/3))","A",14,8,23,0.3478,1,"{1502, 1347, 200, 31, 634, 617, 204, 628}"
28,1,411,0,0.2761763,"\int \frac{x \left(1-x^3\right)}{1-x^3+x^6} \, dx","Int[(x*(1 - x^3))/(1 - x^3 + x^6),x]","\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}","\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}",1,"((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) - ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) - ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) - ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) + ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 + I*Sqrt[3])^(1/3))","A",13,7,21,0.3333,1,"{1510, 292, 31, 634, 617, 204, 628}"
29,1,411,0,0.2767481,"\int \frac{1-x^3}{1-x^3+x^6} \, dx","Int[(1 - x^3)/(1 - x^3 + x^6),x]","\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}","\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}",1,"-((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) - ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) - ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) + ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 + I*Sqrt[3])^(2/3))","A",13,7,20,0.3500,1,"{1422, 200, 31, 634, 617, 204, 628}"
30,1,416,0,0.2754993,"\int \frac{1-x^3}{x^2 \left(1-x^3+x^6\right)} \, dx","Int[(1 - x^3)/(x^2*(1 - x^3 + x^6)),x]","\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{1}{x}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}","\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{1}{x}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}",1,"-x^(-1) - ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) - ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) - ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) + ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 + I*Sqrt[3])^(1/3))","A",14,8,23,0.3478,1,"{1504, 1374, 292, 31, 634, 617, 204, 628}"
31,1,418,0,0.3589255,"\int \frac{1-x^3}{x^3 \left(1-x^3+x^6\right)} \, dx","Int[(1 - x^3)/(x^3*(1 - x^3 + x^6)),x]","-\frac{1}{2 x^2}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}","-\frac{1}{2 x^2}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}",1,"-1/(2*x^2) + ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) - ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) - ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) - ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) + ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 + I*Sqrt[3])^(2/3))","A",15,9,23,0.3913,1,"{1504, 12, 1374, 200, 31, 634, 617, 204, 628}"
32,1,36,0,0.0388101,"\int \frac{x^2 \left(-2+x^3\right)}{1-x^3+x^6} \, dx","Int[(x^2*(-2 + x^3))/(1 - x^3 + x^6),x]","\frac{1}{6} \log \left(x^6-x^3+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{6} \log \left(x^6-x^3+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 - 2*x^3)/Sqrt[3]]/Sqrt[3] + Log[1 - x^3 + x^6]/6","A",5,5,21,0.2381,1,"{1468, 634, 618, 204, 628}"
33,1,39,0,0.0563145,"\int \frac{1+x^3}{x \left(1-x^3+x^6\right)} \, dx","Int[(1 + x^3)/(x*(1 - x^3 + x^6)),x]","-\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{\sqrt{3}}+\log (x)","-\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{\sqrt{3}}+\log (x)",1,"-(ArcTan[(1 - 2*x^3)/Sqrt[3]]/Sqrt[3]) + Log[x] - Log[1 - x^3 + x^6]/6","A",7,6,21,0.2857,1,"{1474, 800, 634, 618, 204, 628}"
34,1,39,0,0.0629689,"\int \frac{1+x^3}{x-x^4+x^7} \, dx","Int[(1 + x^3)/(x - x^4 + x^7),x]","-\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{\sqrt{3}}+\log (x)","-\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{\sqrt{3}}+\log (x)",1,"-(ArcTan[(1 - 2*x^3)/Sqrt[3]]/Sqrt[3]) + Log[x] - Log[1 - x^3 + x^6]/6","A",8,7,18,0.3889,1,"{1594, 1474, 800, 634, 618, 204, 628}"
35,1,396,0,0.4157697,"\int \left(d+e x^3\right)^{5/2} \left(a+b x^3+c x^6\right) \, dx","Int[(d + e*x^3)^(5/2)*(a + b*x^3 + c*x^6),x]","\frac{2 x \left(d+e x^3\right)^{5/2} \left(667 a e^2-58 b d e+16 c d^2\right)}{11339 e^2}+\frac{30 d x \left(d+e x^3\right)^{3/2} \left(667 a e^2-58 b d e+16 c d^2\right)}{124729 e^2}+\frac{54 d^2 x \sqrt{d+e x^3} \left(667 a e^2-58 b d e+16 c d^2\right)}{124729 e^2}+\frac{54\ 3^{3/4} \sqrt{2+\sqrt{3}} d^3 \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(667 a e^2-58 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{124729 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}-\frac{2 x \left(d+e x^3\right)^{7/2} (8 c d-29 b e)}{667 e^2}+\frac{2 c x^4 \left(d+e x^3\right)^{7/2}}{29 e}","\frac{2 x \left(d+e x^3\right)^{5/2} \left(667 a e^2-58 b d e+16 c d^2\right)}{11339 e^2}+\frac{30 d x \left(d+e x^3\right)^{3/2} \left(667 a e^2-58 b d e+16 c d^2\right)}{124729 e^2}+\frac{54 d^2 x \sqrt{d+e x^3} \left(667 a e^2-58 b d e+16 c d^2\right)}{124729 e^2}+\frac{54\ 3^{3/4} \sqrt{2+\sqrt{3}} d^3 \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(667 a e^2-58 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{124729 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}-\frac{2 x \left(d+e x^3\right)^{7/2} (8 c d-29 b e)}{667 e^2}+\frac{2 c x^4 \left(d+e x^3\right)^{7/2}}{29 e}",1,"(54*d^2*(16*c*d^2 - 58*b*d*e + 667*a*e^2)*x*Sqrt[d + e*x^3])/(124729*e^2) + (30*d*(16*c*d^2 - 58*b*d*e + 667*a*e^2)*x*(d + e*x^3)^(3/2))/(124729*e^2) + (2*(16*c*d^2 - 58*b*d*e + 667*a*e^2)*x*(d + e*x^3)^(5/2))/(11339*e^2) - (2*(8*c*d - 29*b*e)*x*(d + e*x^3)^(7/2))/(667*e^2) + (2*c*x^4*(d + e*x^3)^(7/2))/(29*e) + (54*3^(3/4)*Sqrt[2 + Sqrt[3]]*d^3*(16*c*d^2 - 58*b*d*e + 667*a*e^2)*(d^(1/3) + e^(1/3)*x)*Sqrt[(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*d^(1/3) + e^(1/3)*x)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)], -7 - 4*Sqrt[3]])/(124729*e^(7/3)*Sqrt[(d^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*Sqrt[d + e*x^3])","A",6,4,24,0.1667,1,"{1411, 388, 195, 218}"
36,1,356,0,0.3114837,"\int \left(d+e x^3\right)^{3/2} \left(a+b x^3+c x^6\right) \, dx","Int[(d + e*x^3)^(3/2)*(a + b*x^3 + c*x^6),x]","\frac{2 x \left(d+e x^3\right)^{3/2} \left(391 a e^2-46 b d e+16 c d^2\right)}{4301 e^2}+\frac{18 d x \sqrt{d+e x^3} \left(391 a e^2-46 b d e+16 c d^2\right)}{21505 e^2}+\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} d^2 \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(391 a e^2-46 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{21505 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}-\frac{2 x \left(d+e x^3\right)^{5/2} (8 c d-23 b e)}{391 e^2}+\frac{2 c x^4 \left(d+e x^3\right)^{5/2}}{23 e}","\frac{2 x \left(d+e x^3\right)^{3/2} \left(391 a e^2-46 b d e+16 c d^2\right)}{4301 e^2}+\frac{18 d x \sqrt{d+e x^3} \left(391 a e^2-46 b d e+16 c d^2\right)}{21505 e^2}+\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} d^2 \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(391 a e^2-46 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{21505 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}-\frac{2 x \left(d+e x^3\right)^{5/2} (8 c d-23 b e)}{391 e^2}+\frac{2 c x^4 \left(d+e x^3\right)^{5/2}}{23 e}",1,"(18*d*(16*c*d^2 - 46*b*d*e + 391*a*e^2)*x*Sqrt[d + e*x^3])/(21505*e^2) + (2*(16*c*d^2 - 46*b*d*e + 391*a*e^2)*x*(d + e*x^3)^(3/2))/(4301*e^2) - (2*(8*c*d - 23*b*e)*x*(d + e*x^3)^(5/2))/(391*e^2) + (2*c*x^4*(d + e*x^3)^(5/2))/(23*e) + (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*d^2*(16*c*d^2 - 46*b*d*e + 391*a*e^2)*(d^(1/3) + e^(1/3)*x)*Sqrt[(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*d^(1/3) + e^(1/3)*x)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)], -7 - 4*Sqrt[3]])/(21505*e^(7/3)*Sqrt[(d^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*Sqrt[d + e*x^3])","A",5,4,24,0.1667,1,"{1411, 388, 195, 218}"
37,1,316,0,0.2462139,"\int \sqrt{d+e x^3} \left(a+b x^3+c x^6\right) \, dx","Int[Sqrt[d + e*x^3]*(a + b*x^3 + c*x^6),x]","\frac{2 x \sqrt{d+e x^3} \left(187 a e^2-34 b d e+16 c d^2\right)}{935 e^2}+\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} d \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(187 a e^2-34 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{935 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}-\frac{2 x \left(d+e x^3\right)^{3/2} (8 c d-17 b e)}{187 e^2}+\frac{2 c x^4 \left(d+e x^3\right)^{3/2}}{17 e}","\frac{2 x \sqrt{d+e x^3} \left(187 a e^2-34 b d e+16 c d^2\right)}{935 e^2}+\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} d \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(187 a e^2-34 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{935 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}-\frac{2 x \left(d+e x^3\right)^{3/2} (8 c d-17 b e)}{187 e^2}+\frac{2 c x^4 \left(d+e x^3\right)^{3/2}}{17 e}",1,"(2*(16*c*d^2 - 34*b*d*e + 187*a*e^2)*x*Sqrt[d + e*x^3])/(935*e^2) - (2*(8*c*d - 17*b*e)*x*(d + e*x^3)^(3/2))/(187*e^2) + (2*c*x^4*(d + e*x^3)^(3/2))/(17*e) + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*d*(16*c*d^2 - 34*b*d*e + 187*a*e^2)*(d^(1/3) + e^(1/3)*x)*Sqrt[(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*d^(1/3) + e^(1/3)*x)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)], -7 - 4*Sqrt[3]])/(935*e^(7/3)*Sqrt[(d^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*Sqrt[d + e*x^3])","A",4,4,24,0.1667,1,"{1411, 388, 195, 218}"
38,1,278,0,0.1823361,"\int \frac{a+b x^3+c x^6}{\sqrt{d+e x^3}} \, dx","Int[(a + b*x^3 + c*x^6)/Sqrt[d + e*x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(55 a e^2-22 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}-\frac{2 x \sqrt{d+e x^3} (8 c d-11 b e)}{55 e^2}+\frac{2 c x^4 \sqrt{d+e x^3}}{11 e}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(55 a e^2-22 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}-\frac{2 x \sqrt{d+e x^3} (8 c d-11 b e)}{55 e^2}+\frac{2 c x^4 \sqrt{d+e x^3}}{11 e}",1,"(-2*(8*c*d - 11*b*e)*x*Sqrt[d + e*x^3])/(55*e^2) + (2*c*x^4*Sqrt[d + e*x^3])/(11*e) + (2*Sqrt[2 + Sqrt[3]]*(16*c*d^2 - 22*b*d*e + 55*a*e^2)*(d^(1/3) + e^(1/3)*x)*Sqrt[(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*d^(1/3) + e^(1/3)*x)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)], -7 - 4*Sqrt[3]])/(55*3^(1/4)*e^(7/3)*Sqrt[(d^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*Sqrt[d + e*x^3])","A",3,3,24,0.1250,1,"{1411, 388, 218}"
39,1,289,0,0.1890062,"\int \frac{a+b x^3+c x^6}{\left(d+e x^3\right)^{3/2}} \, dx","Int[(a + b*x^3 + c*x^6)/(d + e*x^3)^(3/2),x]","\frac{2 x \left(a e^2-b d e+c d^2\right)}{3 d e^2 \sqrt{d+e x^3}}-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(16 c d^2-5 e (a e+2 b d)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} d e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}+\frac{2 c x \sqrt{d+e x^3}}{5 e^2}","\frac{2 x \left(a e^2-b d e+c d^2\right)}{3 d e^2 \sqrt{d+e x^3}}-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(16 c d^2-5 e (a e+2 b d)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} d e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}+\frac{2 c x \sqrt{d+e x^3}}{5 e^2}",1,"(2*(c*d^2 - b*d*e + a*e^2)*x)/(3*d*e^2*Sqrt[d + e*x^3]) + (2*c*x*Sqrt[d + e*x^3])/(5*e^2) - (2*Sqrt[2 + Sqrt[3]]*(16*c*d^2 - 5*e*(2*b*d + a*e))*(d^(1/3) + e^(1/3)*x)*Sqrt[(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*d^(1/3) + e^(1/3)*x)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)], -7 - 4*Sqrt[3]])/(15*3^(1/4)*d*e^(7/3)*Sqrt[(d^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*Sqrt[d + e*x^3])","A",3,3,24,0.1250,1,"{1409, 388, 218}"
40,1,309,0,0.2106586,"\int \frac{a+b x^3+c x^6}{\left(d+e x^3\right)^{5/2}} \, dx","Int[(a + b*x^3 + c*x^6)/(d + e*x^3)^(5/2),x]","-\frac{2 x \left(-7 a e^2-2 b d e+11 c d^2\right)}{27 d^2 e^2 \sqrt{d+e x^3}}+\frac{2 x \left(a e^2-b d e+c d^2\right)}{9 d e^2 \left(d+e x^3\right)^{3/2}}+\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(e (7 a e+2 b d)+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} d^2 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}","-\frac{2 x \left(-7 a e^2-2 b d e+11 c d^2\right)}{27 d^2 e^2 \sqrt{d+e x^3}}+\frac{2 x \left(a e^2-b d e+c d^2\right)}{9 d e^2 \left(d+e x^3\right)^{3/2}}+\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(e (7 a e+2 b d)+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} d^2 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}",1,"(2*(c*d^2 - b*d*e + a*e^2)*x)/(9*d*e^2*(d + e*x^3)^(3/2)) - (2*(11*c*d^2 - 2*b*d*e - 7*a*e^2)*x)/(27*d^2*e^2*Sqrt[d + e*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(16*c*d^2 + e*(2*b*d + 7*a*e))*(d^(1/3) + e^(1/3)*x)*Sqrt[(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*d^(1/3) + e^(1/3)*x)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*d^2*e^(7/3)*Sqrt[(d^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*Sqrt[d + e*x^3])","A",3,3,24,0.1250,1,"{1409, 385, 218}"
41,1,349,0,0.3240334,"\int \frac{a+b x^3+c x^6}{\left(d+e x^3\right)^{7/2}} \, dx","Int[(a + b*x^3 + c*x^6)/(d + e*x^3)^(7/2),x]","\frac{2 x \left(91 a e^2+14 b d e+16 c d^2\right)}{405 d^3 e^2 \sqrt{d+e x^3}}-\frac{2 x \left(-13 a e^2-2 b d e+17 c d^2\right)}{135 d^2 e^2 \left(d+e x^3\right)^{3/2}}+\frac{2 x \left(a e^2-b d e+c d^2\right)}{15 d e^2 \left(d+e x^3\right)^{5/2}}+\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(91 a e^2+14 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{405 \sqrt[4]{3} d^3 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}","\frac{2 x \left(91 a e^2+14 b d e+16 c d^2\right)}{405 d^3 e^2 \sqrt{d+e x^3}}-\frac{2 x \left(-13 a e^2-2 b d e+17 c d^2\right)}{135 d^2 e^2 \left(d+e x^3\right)^{3/2}}+\frac{2 x \left(a e^2-b d e+c d^2\right)}{15 d e^2 \left(d+e x^3\right)^{5/2}}+\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(91 a e^2+14 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{405 \sqrt[4]{3} d^3 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}",1,"(2*(c*d^2 - b*d*e + a*e^2)*x)/(15*d*e^2*(d + e*x^3)^(5/2)) - (2*(17*c*d^2 - 2*b*d*e - 13*a*e^2)*x)/(135*d^2*e^2*(d + e*x^3)^(3/2)) + (2*(16*c*d^2 + 14*b*d*e + 91*a*e^2)*x)/(405*d^3*e^2*Sqrt[d + e*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(16*c*d^2 + 14*b*d*e + 91*a*e^2)*(d^(1/3) + e^(1/3)*x)*Sqrt[(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*d^(1/3) + e^(1/3)*x)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)], -7 - 4*Sqrt[3]])/(405*3^(1/4)*d^3*e^(7/3)*Sqrt[(d^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*Sqrt[d + e*x^3])","A",4,4,24,0.1667,1,"{1409, 385, 199, 218}"
42,1,389,0,0.394819,"\int \frac{a+b x^3+c x^6}{\left(d+e x^3\right)^{9/2}} \, dx","Int[(a + b*x^3 + c*x^6)/(d + e*x^3)^(9/2),x]","\frac{2 x \left(247 a e^2+26 b d e+16 c d^2\right)}{1215 d^4 e^2 \sqrt{d+e x^3}}+\frac{2 x \left(247 a e^2+26 b d e+16 c d^2\right)}{2835 d^3 e^2 \left(d+e x^3\right)^{3/2}}-\frac{2 x \left(-19 a e^2-2 b d e+23 c d^2\right)}{315 d^2 e^2 \left(d+e x^3\right)^{5/2}}+\frac{2 x \left(a e^2-b d e+c d^2\right)}{21 d e^2 \left(d+e x^3\right)^{7/2}}+\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(247 a e^2+26 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{1215 \sqrt[4]{3} d^4 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}","\frac{2 x \left(247 a e^2+26 b d e+16 c d^2\right)}{1215 d^4 e^2 \sqrt{d+e x^3}}+\frac{2 x \left(247 a e^2+26 b d e+16 c d^2\right)}{2835 d^3 e^2 \left(d+e x^3\right)^{3/2}}-\frac{2 x \left(-19 a e^2-2 b d e+23 c d^2\right)}{315 d^2 e^2 \left(d+e x^3\right)^{5/2}}+\frac{2 x \left(a e^2-b d e+c d^2\right)}{21 d e^2 \left(d+e x^3\right)^{7/2}}+\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \sqrt{\frac{d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \left(247 a e^2+26 b d e+16 c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{e} x+\left(1-\sqrt{3}\right) \sqrt[3]{d}}{\sqrt[3]{e} x+\left(1+\sqrt{3}\right) \sqrt[3]{d}}\right)|-7-4 \sqrt{3}\right)}{1215 \sqrt[4]{3} d^4 e^{7/3} \sqrt{\frac{\sqrt[3]{d} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{d}+\sqrt[3]{e} x\right)^2}} \sqrt{d+e x^3}}",1,"(2*(c*d^2 - b*d*e + a*e^2)*x)/(21*d*e^2*(d + e*x^3)^(7/2)) - (2*(23*c*d^2 - 2*b*d*e - 19*a*e^2)*x)/(315*d^2*e^2*(d + e*x^3)^(5/2)) + (2*(16*c*d^2 + 26*b*d*e + 247*a*e^2)*x)/(2835*d^3*e^2*(d + e*x^3)^(3/2)) + (2*(16*c*d^2 + 26*b*d*e + 247*a*e^2)*x)/(1215*d^4*e^2*Sqrt[d + e*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(16*c*d^2 + 26*b*d*e + 247*a*e^2)*(d^(1/3) + e^(1/3)*x)*Sqrt[(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*d^(1/3) + e^(1/3)*x)/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)], -7 - 4*Sqrt[3]])/(1215*3^(1/4)*d^4*e^(7/3)*Sqrt[(d^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + Sqrt[3])*d^(1/3) + e^(1/3)*x)^2]*Sqrt[d + e*x^3])","A",5,4,24,0.1667,1,"{1409, 385, 199, 218}"
43,1,433,0,1.1323195,"\int \frac{x^4 \left(d+e x^4\right)}{a+b x^4+c x^8} \, dx","Int[(x^4*(d + e*x^4))/(a + b*x^4 + c*x^8),x]","-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{e x}{c}","-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{e x}{c}",1,"(e*x)/c - ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - ((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) - ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - ((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",8,5,25,0.2000,1,"{1502, 1422, 212, 208, 205}"
44,1,72,0,0.0721409,"\int \frac{x^3 \left(d+e x^4\right)}{a+b x^4+c x^8} \, dx","Int[(x^3*(d + e*x^4))/(a + b*x^4 + c*x^8),x]","\frac{e \log \left(a+b x^4+c x^8\right)}{8 c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 c \sqrt{b^2-4 a c}}","\frac{e \log \left(a+b x^4+c x^8\right)}{8 c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 c \sqrt{b^2-4 a c}}",1,"-((2*c*d - b*e)*ArcTanh[(b + 2*c*x^4)/Sqrt[b^2 - 4*a*c]])/(4*c*Sqrt[b^2 - 4*a*c]) + (e*Log[a + b*x^4 + c*x^8])/(8*c)","A",5,5,25,0.2000,1,"{1468, 634, 618, 206, 628}"
45,1,375,0,0.4557758,"\int \frac{x^2 \left(d+e x^4\right)}{a+b x^4+c x^8} \, dx","Int[(x^2*(d + e*x^4))/(a + b*x^4 + c*x^8),x]","\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}","\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}",1,"((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(3/4)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(3/4)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(3/4)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(3/4)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",7,4,25,0.1600,1,"{1510, 298, 205, 208}"
46,1,184,0,0.2128058,"\int \frac{x \left(d+e x^4\right)}{a+b x^4+c x^8} \, dx","Int[(x*(d + e*x^4))/(a + b*x^4 + c*x^8),x]","\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,23,0.1304,1,"{1490, 1166, 205}"
47,1,375,0,0.3509823,"\int \frac{d+e x^4}{a+b x^4+c x^8} \, dx","Int[(d + e*x^4)/(a + b*x^4 + c*x^8),x]","-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}","-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}",1,"-((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(1/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(1/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(1/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(1/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",7,4,22,0.1818,1,"{1422, 212, 208, 205}"
48,1,78,0,0.1255433,"\int \frac{d+e x^4}{x \left(a+b x^4+c x^8\right)} \, dx","Int[(d + e*x^4)/(x*(a + b*x^4 + c*x^8)),x]","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 a \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b x^4+c x^8\right)}{8 a}+\frac{d \log (x)}{a}","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 a \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b x^4+c x^8\right)}{8 a}+\frac{d \log (x)}{a}",1,"((b*d - 2*a*e)*ArcTanh[(b + 2*c*x^4)/Sqrt[b^2 - 4*a*c]])/(4*a*Sqrt[b^2 - 4*a*c]) + (d*Log[x])/a - (d*Log[a + b*x^4 + c*x^8])/(8*a)","A",7,6,25,0.2400,1,"{1474, 800, 634, 618, 206, 628}"
49,1,392,0,0.6827749,"\int \frac{d+e x^4}{x^2 \left(a+b x^4+c x^8\right)} \, dx","Int[(d + e*x^4)/(x^2*(a + b*x^4 + c*x^8)),x]","-\frac{\sqrt[4]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{d}{a x}","-\frac{\sqrt[4]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{d}{a x}",1,"-(d/(a*x)) - (c^(1/4)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",8,5,25,0.2000,1,"{1504, 1510, 298, 205, 208}"
50,1,199,0,0.3113091,"\int \frac{d+e x^4}{x^3 \left(a+b x^4+c x^8\right)} \, dx","Int[(d + e*x^4)/(x^3*(a + b*x^4 + c*x^8)),x]","-\frac{\sqrt{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{d}{2 a x^2}","-\frac{\sqrt{c} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{d}{2 a x^2}",1,"-d/(2*a*x^2) - (Sqrt[c]*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,25,0.1600,1,"{1490, 1281, 1166, 205}"
51,1,394,0,0.6252474,"\int \frac{d+e x^4}{x^4 \left(a+b x^4+c x^8\right)} \, dx","Int[(d + e*x^4)/(x^4*(a + b*x^4 + c*x^8)),x]","\frac{c^{3/4} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{d}{3 a x^3}","\frac{c^{3/4} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{d}{3 a x^3}",1,"-d/(3*a*x^3) + (c^(3/4)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",8,5,25,0.2000,1,"{1504, 1422, 212, 208, 205}"
52,1,278,0,0.2995735,"\int \frac{x^4 \left(1-x^4\right)}{1-x^4+x^8} \, dx","Int[(x^4*(1 - x^4))/(1 - x^4 + x^8),x]","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-x-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-x-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}",1,"-x - ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) - ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) + ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) + ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) - Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) - Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6])","A",20,7,23,0.3043,1,"{1502, 1346, 1169, 634, 618, 204, 628}"
53,1,39,0,0.0423471,"\int \frac{x^3 \left(1-x^4\right)}{1-x^4+x^8} \, dx","Int[(x^3*(1 - x^4))/(1 - x^4 + x^8),x]","-\frac{1}{8} \log \left(x^8-x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}","-\frac{1}{8} \log \left(x^8-x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) - Log[1 - x^4 + x^8]/8","A",5,5,23,0.2174,1,"{1468, 634, 618, 204, 628}"
54,1,355,0,0.289485,"\int \frac{x^2 \left(1-x^4\right)}{1-x^4+x^8} \, dx","Int[(x^2*(1 - x^4))/(1 - x^4 + x^8),x]","\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}","\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}",1,"ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) - ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) - ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) + ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) + (Sqrt[(2 - Sqrt[3])/3]*Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 - Sqrt[3])/3]*Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 + Sqrt[3])/3]*Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2])/8 + (Sqrt[(2 + Sqrt[3])/3]*Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2])/8","A",21,7,23,0.3043,1,"{1506, 1279, 1169, 634, 618, 204, 628}"
55,1,50,0,0.0399463,"\int \frac{x \left(1-x^4\right)}{1-x^4+x^8} \, dx","Int[(x*(1 - x^4))/(1 - x^4 + x^8),x]","\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{4 \sqrt{3}}","\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{4 \sqrt{3}}",1,"-Log[1 - Sqrt[3]*x^2 + x^4]/(4*Sqrt[3]) + Log[1 + Sqrt[3]*x^2 + x^4]/(4*Sqrt[3])","A",4,3,21,0.1429,1,"{1490, 1164, 628}"
56,1,355,0,0.216203,"\int \frac{1-x^4}{1-x^4+x^8} \, dx","Int[(1 - x^4)/(1 - x^4 + x^8),x]","\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}","\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}",1,"-ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) + ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) + ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) - ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) + (Sqrt[(2 - Sqrt[3])/3]*Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 - Sqrt[3])/3]*Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 + Sqrt[3])/3]*Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2])/8 + (Sqrt[(2 + Sqrt[3])/3]*Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2])/8","A",19,6,20,0.3000,1,"{1421, 1169, 634, 618, 204, 628}"
57,1,41,0,0.0526827,"\int \frac{1-x^4}{x \left(1-x^4+x^8\right)} \, dx","Int[(1 - x^4)/(x*(1 - x^4 + x^8)),x]","-\frac{1}{8} \log \left(x^8-x^4+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\log (x)","-\frac{1}{8} \log \left(x^8-x^4+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\log (x)",1,"ArcTan[(1 - 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) + Log[x] - Log[1 - x^4 + x^8]/8","A",7,6,23,0.2609,1,"{1474, 800, 634, 618, 204, 628}"
58,1,280,0,0.2079928,"\int \frac{1-x^4}{x^2 \left(1-x^4+x^8\right)} \, dx","Int[(1 - x^4)/(x^2*(1 - x^4 + x^8)),x]","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}",1,"-x^(-1) + ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) + ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) - ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) - ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) - Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) - Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6])","A",20,7,23,0.3043,1,"{1504, 1372, 1169, 634, 618, 204, 628}"
59,1,89,0,0.0903328,"\int \frac{1-x^4}{x^3 \left(1-x^4+x^8\right)} \, dx","Int[(1 - x^4)/(x^3*(1 - x^4 + x^8)),x]","-\frac{1}{2 x^2}-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x^2\right)-\frac{1}{4} \tan ^{-1}\left(2 x^2+\sqrt{3}\right)","-\frac{1}{2 x^2}-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x^2\right)-\frac{1}{4} \tan ^{-1}\left(2 x^2+\sqrt{3}\right)",1,"-1/(2*x^2) + ArcTan[Sqrt[3] - 2*x^2]/4 - ArcTan[Sqrt[3] + 2*x^2]/4 - Log[1 - Sqrt[3]*x^2 + x^4]/(8*Sqrt[3]) + Log[1 + Sqrt[3]*x^2 + x^4]/(8*Sqrt[3])","A",11,8,23,0.3478,1,"{1490, 1281, 1127, 1161, 618, 204, 1164, 628}"
60,1,370,0,0.2691246,"\int \frac{1-x^4}{x^4 \left(1-x^4+x^8\right)} \, dx","Int[(1 - x^4)/(x^4*(1 - x^4 + x^8)),x]","-\frac{1}{3 x^3}+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)","-\frac{1}{3 x^3}+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)",1,"-1/(3*x^3) - (Sqrt[(2 - Sqrt[3])/3]*ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]])/4 + (Sqrt[(2 + Sqrt[3])/3]*ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]])/4 + (Sqrt[(2 - Sqrt[3])/3]*ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]])/4 - (Sqrt[(2 + Sqrt[3])/3]*ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]])/4 + (Sqrt[(2 + Sqrt[3])/3]*Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 + Sqrt[3])/3]*Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 - Sqrt[3])/3]*Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2])/8 + (Sqrt[(2 - Sqrt[3])/3]*Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2])/8","A",21,9,23,0.3913,1,"{1504, 12, 1373, 1127, 1161, 618, 204, 1164, 628}"
61,1,280,0,0.5973695,"\int \frac{x^3}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) (d+e x)} \, dx","Int[x^3/((a + c/x^2 + b/x)*(d + e*x)),x]","\frac{\left(a^2 c^2 d-3 a b^2 c d+2 a b c^2 e-b^3 c e+b^4 d\right) \log \left(a x^2+b x+c\right)}{2 a^4 \left(a d^2-e (b d-c e)\right)}+\frac{\left(5 a^2 b c^2 d-2 a^2 c^3 e+4 a b^2 c^2 e-5 a b^3 c d-b^4 c e+b^5 d\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^4 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{x \left(a^2 d^2+a e (b d-c e)+b^2 e^2\right)}{a^3 e^3}-\frac{x^2 (a d+b e)}{2 a^2 e^2}-\frac{d^5 \log (d+e x)}{e^4 \left(a d^2-e (b d-c e)\right)}+\frac{x^3}{3 a e}","\frac{\left(a^2 c^2 d-3 a b^2 c d+2 a b c^2 e-b^3 c e+b^4 d\right) \log \left(a x^2+b x+c\right)}{2 a^4 \left(a d^2-e (b d-c e)\right)}+\frac{\left(5 a^2 b c^2 d-2 a^2 c^3 e+4 a b^2 c^2 e-5 a b^3 c d-b^4 c e+b^5 d\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^4 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{x \left(a^2 d^2+a e (b d-c e)+b^2 e^2\right)}{a^3 e^3}-\frac{x^2 (a d+b e)}{2 a^2 e^2}-\frac{d^5 \log (d+e x)}{e^4 \left(a d^2-e (b d-c e)\right)}+\frac{x^3}{3 a e}",1,"((a^2*d^2 + b^2*e^2 + a*e*(b*d - c*e))*x)/(a^3*e^3) - ((a*d + b*e)*x^2)/(2*a^2*e^2) + x^3/(3*a*e) + ((b^5*d - 5*a*b^3*c*d + 5*a^2*b*c^2*d - b^4*c*e + 4*a*b^2*c^2*e - 2*a^2*c^3*e)*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(a^4*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))) - (d^5*Log[d + e*x])/(e^4*(a*d^2 - e*(b*d - c*e))) + ((b^4*d - 3*a*b^2*c*d + a^2*c^2*d - b^3*c*e + 2*a*b*c^2*e)*Log[c + b*x + a*x^2])/(2*a^4*(a*d^2 - e*(b*d - c*e)))","A",7,6,25,0.2400,1,"{1569, 1628, 634, 618, 206, 628}"
62,1,218,0,0.395218,"\int \frac{x^2}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) (d+e x)} \, dx","Int[x^2/((a + c/x^2 + b/x)*(d + e*x)),x]","-\frac{\left(-2 a b c d+a c^2 e-b^2 c e+b^3 d\right) \log \left(a x^2+b x+c\right)}{2 a^3 \left(a d^2-e (b d-c e)\right)}-\frac{\left(2 a^2 c^2 d-4 a b^2 c d+3 a b c^2 e-b^3 c e+b^4 d\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}-\frac{x (a d+b e)}{a^2 e^2}+\frac{d^4 \log (d+e x)}{e^3 \left(a d^2-e (b d-c e)\right)}+\frac{x^2}{2 a e}","-\frac{\left(-2 a b c d+a c^2 e-b^2 c e+b^3 d\right) \log \left(a x^2+b x+c\right)}{2 a^3 \left(a d^2-e (b d-c e)\right)}-\frac{\left(2 a^2 c^2 d-4 a b^2 c d+3 a b c^2 e-b^3 c e+b^4 d\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}-\frac{x (a d+b e)}{a^2 e^2}+\frac{d^4 \log (d+e x)}{e^3 \left(a d^2-e (b d-c e)\right)}+\frac{x^2}{2 a e}",1,"-(((a*d + b*e)*x)/(a^2*e^2)) + x^2/(2*a*e) - ((b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d - b^3*c*e + 3*a*b*c^2*e)*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(a^3*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))) + (d^4*Log[d + e*x])/(e^3*(a*d^2 - e*(b*d - c*e))) - ((b^3*d - 2*a*b*c*d - b^2*c*e + a*c^2*e)*Log[c + b*x + a*x^2])/(2*a^3*(a*d^2 - e*(b*d - c*e)))","A",7,6,25,0.2400,1,"{1569, 1628, 634, 618, 206, 628}"
63,1,176,0,0.2852689,"\int \frac{x}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) (d+e x)} \, dx","Int[x/((a + c/x^2 + b/x)*(d + e*x)),x]","\frac{\left(-3 a b c d+2 a c^2 e-b^2 c e+b^3 d\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{\left(-a c d+b^2 d-b c e\right) \log \left(a x^2+b x+c\right)}{2 a^2 \left(a d^2-e (b d-c e)\right)}-\frac{d^3 \log (d+e x)}{e^2 \left(a d^2-e (b d-c e)\right)}+\frac{x}{a e}","\frac{\left(-3 a b c d+2 a c^2 e-b^2 c e+b^3 d\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{\left(-a c d+b^2 d-b c e\right) \log \left(a x^2+b x+c\right)}{2 a^2 \left(a d^2-e (b d-c e)\right)}-\frac{d^3 \log (d+e x)}{e^2 \left(a d^2-e (b d-c e)\right)}+\frac{x}{a e}",1,"x/(a*e) + ((b^3*d - 3*a*b*c*d - b^2*c*e + 2*a*c^2*e)*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(a^2*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))) - (d^3*Log[d + e*x])/(e^2*(a*d^2 - e*(b*d - c*e))) + ((b^2*d - a*c*d - b*c*e)*Log[c + b*x + a*x^2])/(2*a^2*(a*d^2 - e*(b*d - c*e)))","A",7,6,23,0.2609,1,"{1569, 1628, 634, 618, 206, 628}"
64,1,149,0,0.210117,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) (d+e x)} \, dx","Int[1/((a + c/x^2 + b/x)*(d + e*x)),x]","-\frac{\left(-2 a c d+b^2 d-b c e\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{d^2 \log (d+e x)}{e \left(a d^2-b d e+c e^2\right)}-\frac{(b d-c e) \log \left(a x^2+b x+c\right)}{2 a \left(a d^2-e (b d-c e)\right)}","-\frac{\left(-2 a c d+b^2 d-b c e\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{d^2 \log (d+e x)}{e \left(a d^2-b d e+c e^2\right)}-\frac{(b d-c e) \log \left(a x^2+b x+c\right)}{2 a \left(a d^2-e (b d-c e)\right)}",1,"-(((b^2*d - 2*a*c*d - b*c*e)*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e)))) + (d^2*Log[d + e*x])/(e*(a*d^2 - b*d*e + c*e^2)) - ((b*d - c*e)*Log[c + b*x + a*x^2])/(2*a*(a*d^2 - e*(b*d - c*e)))","A",7,6,22,0.2727,1,"{1445, 1628, 634, 618, 206, 628}"
65,1,124,0,0.1449501,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x (d+e x)} \, dx","Int[1/((a + c/x^2 + b/x)*x*(d + e*x)),x]","\frac{(b d-2 c e) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{d \log \left(a x^2+b x+c\right)}{2 \left(a d^2-e (b d-c e)\right)}-\frac{d \log (d+e x)}{a d^2-e (b d-c e)}","\frac{(b d-2 c e) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{d \log \left(a x^2+b x+c\right)}{2 \left(a d^2-e (b d-c e)\right)}-\frac{d \log (d+e x)}{a d^2-e (b d-c e)}",1,"((b*d - 2*c*e)*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))) - (d*Log[d + e*x])/(a*d^2 - e*(b*d - c*e)) + (d*Log[c + b*x + a*x^2])/(2*(a*d^2 - e*(b*d - c*e)))","A",7,6,25,0.2400,1,"{1569, 800, 634, 618, 206, 628}"
66,1,123,0,0.1071724,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x^2 (d+e x)} \, dx","Int[1/((a + c/x^2 + b/x)*x^2*(d + e*x)),x]","-\frac{(2 a d-b e) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}-\frac{e \log \left(a x^2+b x+c\right)}{2 \left(a d^2-b d e+c e^2\right)}+\frac{e \log (d+e x)}{a d^2-b d e+c e^2}","-\frac{(2 a d-b e) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}-\frac{e \log \left(a x^2+b x+c\right)}{2 \left(a d^2-b d e+c e^2\right)}+\frac{e \log (d+e x)}{a d^2-b d e+c e^2}",1,"-(((2*a*d - b*e)*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e)))) + (e*Log[d + e*x])/(a*d^2 - b*d*e + c*e^2) - (e*Log[c + b*x + a*x^2])/(2*(a*d^2 - b*d*e + c*e^2))","A",7,7,25,0.2800,1,"{1569, 705, 31, 634, 618, 206, 628}"
67,1,159,0,0.2707583,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x^3 (d+e x)} \, dx","Int[1/((a + c/x^2 + b/x)*x^3*(d + e*x)),x]","\frac{\left(a b d+2 a c e+b^2 (-e)\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}-\frac{e^2 \log (d+e x)}{d \left(a d^2-e (b d-c e)\right)}-\frac{(a d-b e) \log \left(a x^2+b x+c\right)}{2 c \left(a d^2-e (b d-c e)\right)}+\frac{\log (x)}{c d}","\frac{\left(a b d+2 a c e+b^2 (-e)\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}-\frac{e^2 \log (d+e x)}{d \left(a d^2-b d e+c e^2\right)}-\frac{(a d-b e) \log \left(a x^2+b x+c\right)}{2 c \left(a d^2-e (b d-c e)\right)}+\frac{\log (x)}{c d}",1,"((a*b*d - b^2*e + 2*a*c*e)*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))) + Log[x]/(c*d) - (e^2*Log[d + e*x])/(d*(a*d^2 - e*(b*d - c*e))) - ((a*d - b*e)*Log[c + b*x + a*x^2])/(2*c*(a*d^2 - e*(b*d - c*e)))","A",7,6,25,0.2400,1,"{1569, 893, 634, 618, 206, 628}"
68,1,193,0,0.3430941,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x^4 (d+e x)} \, dx","Int[1/((a + c/x^2 + b/x)*x^4*(d + e*x)),x]","\frac{\left(2 a^2 c d-a b (b d+3 c e)+b^3 e\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{\left(a b d+a c e+b^2 (-e)\right) \log \left(a x^2+b x+c\right)}{2 c^2 \left(a d^2-e (b d-c e)\right)}+\frac{e^3 \log (d+e x)}{d^2 \left(a d^2-e (b d-c e)\right)}-\frac{\log (x) (b d+c e)}{c^2 d^2}-\frac{1}{c d x}","\frac{\left(2 a^2 c d-a b (b d+3 c e)+b^3 e\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{\left(a b d+a c e+b^2 (-e)\right) \log \left(a x^2+b x+c\right)}{2 c^2 \left(a d^2-e (b d-c e)\right)}+\frac{e^3 \log (d+e x)}{d^2 \left(a d^2-e (b d-c e)\right)}-\frac{\log (x) (b d+c e)}{c^2 d^2}-\frac{1}{c d x}",1,"-(1/(c*d*x)) + ((2*a^2*c*d + b^3*e - a*b*(b*d + 3*c*e))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))) - ((b*d + c*e)*Log[x])/(c^2*d^2) + (e^3*Log[d + e*x])/(d^2*(a*d^2 - e*(b*d - c*e))) + ((a*b*d - b^2*e + a*c*e)*Log[c + b*x + a*x^2])/(2*c^2*(a*d^2 - e*(b*d - c*e)))","A",7,6,25,0.2400,1,"{1569, 893, 634, 618, 206, 628}"
69,1,252,0,0.4284309,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x^5 (d+e x)} \, dx","Int[1/((a + c/x^2 + b/x)*x^5*(d + e*x)),x]","\frac{\left(a^2 c d-a b (b d+2 c e)+b^3 e\right) \log \left(a x^2+b x+c\right)}{2 c^3 \left(a d^2-e (b d-c e)\right)}-\frac{\left(a^2 c (3 b d+2 c e)-a b^2 (b d+4 c e)+b^4 e\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{\log (x) \left(-c \left(a d^2-c e^2\right)+b^2 d^2+b c d e\right)}{c^3 d^3}-\frac{e^4 \log (d+e x)}{d^3 \left(a d^2-e (b d-c e)\right)}+\frac{b d+c e}{c^2 d^2 x}-\frac{1}{2 c d x^2}","\frac{\left(a^2 c d-a b (b d+2 c e)+b^3 e\right) \log \left(a x^2+b x+c\right)}{2 c^3 \left(a d^2-e (b d-c e)\right)}-\frac{\left(a^2 c (3 b d+2 c e)-a b^2 (b d+4 c e)+b^4 e\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)}+\frac{\log (x) \left(-c \left(a d^2-c e^2\right)+b^2 d^2+b c d e\right)}{c^3 d^3}-\frac{e^4 \log (d+e x)}{d^3 \left(a d^2-e (b d-c e)\right)}+\frac{b d+c e}{c^2 d^2 x}-\frac{1}{2 c d x^2}",1,"-1/(2*c*d*x^2) + (b*d + c*e)/(c^2*d^2*x) - ((b^4*e + a^2*c*(3*b*d + 2*c*e) - a*b^2*(b*d + 4*c*e))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))) + ((b^2*d^2 + b*c*d*e - c*(a*d^2 - c*e^2))*Log[x])/(c^3*d^3) - (e^4*Log[d + e*x])/(d^3*(a*d^2 - e*(b*d - c*e))) + ((a^2*c*d + b^3*e - a*b*(b*d + 2*c*e))*Log[c + b*x + a*x^2])/(2*c^3*(a*d^2 - e*(b*d - c*e)))","A",7,6,25,0.2400,1,"{1569, 893, 634, 618, 206, 628}"
70,1,343,0,0.9073762,"\int \frac{x^3}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) (d+e x)^2} \, dx","Int[x^3/((a + c/x^2 + b/x)*(d + e*x)^2),x]","\frac{\left(-b^2 c \left(3 a d^2-c e^2\right)+4 a b c^2 d e+a c^2 \left(a d^2-c e^2\right)-2 b^3 c d e+b^4 d^2\right) \log \left(a x^2+b x+c\right)}{2 a^3 \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(-4 a^2 c^3 d e+8 a b^2 c^2 d e-b^3 c \left(5 a d^2-c e^2\right)+a b c^2 \left(5 a d^2-3 c e^2\right)-2 b^4 c d e+b^5 d^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}-\frac{x (2 a d+b e)}{a^2 e^3}+\frac{d^5}{e^4 (d+e x) \left(a d^2-e (b d-c e)\right)}+\frac{d^4 \log (d+e x) \left(3 a d^2-e (4 b d-5 c e)\right)}{e^4 \left(a d^2-e (b d-c e)\right)^2}+\frac{x^2}{2 a e^2}","\frac{\left(-b^2 c \left(3 a d^2-c e^2\right)+4 a b c^2 d e+a c^2 \left(a d^2-c e^2\right)-2 b^3 c d e+b^4 d^2\right) \log \left(a x^2+b x+c\right)}{2 a^3 \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(-4 a^2 c^3 d e+8 a b^2 c^2 d e-b^3 c \left(5 a d^2-c e^2\right)+a b c^2 \left(5 a d^2-3 c e^2\right)-2 b^4 c d e+b^5 d^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}-\frac{x (2 a d+b e)}{a^2 e^3}+\frac{d^5}{e^4 (d+e x) \left(a d^2-e (b d-c e)\right)}+\frac{d^4 \log (d+e x) \left(3 a d^2-e (4 b d-5 c e)\right)}{e^4 \left(a d^2-e (b d-c e)\right)^2}+\frac{x^2}{2 a e^2}",1,"-(((2*a*d + b*e)*x)/(a^2*e^3)) + x^2/(2*a*e^2) + d^5/(e^4*(a*d^2 - e*(b*d - c*e))*(d + e*x)) + ((b^5*d^2 - 2*b^4*c*d*e + 8*a*b^2*c^2*d*e - 4*a^2*c^3*d*e + a*b*c^2*(5*a*d^2 - 3*c*e^2) - b^3*c*(5*a*d^2 - c*e^2))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(a^3*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) + (d^4*(3*a*d^2 - e*(4*b*d - 5*c*e))*Log[d + e*x])/(e^4*(a*d^2 - e*(b*d - c*e))^2) + ((b^4*d^2 - 2*b^3*c*d*e + 4*a*b*c^2*d*e + a*c^2*(a*d^2 - c*e^2) - b^2*c*(3*a*d^2 - c*e^2))*Log[c + b*x + a*x^2])/(2*a^3*(a*d^2 - e*(b*d - c*e))^2)","A",7,6,25,0.2400,1,"{1569, 1628, 634, 618, 206, 628}"
71,1,274,0,0.5630698,"\int \frac{x^2}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) (d+e x)^2} \, dx","Int[x^2/((a + c/x^2 + b/x)*(d + e*x)^2),x]","-\frac{\left(-b^2 c \left(4 a d^2-c e^2\right)+6 a b c^2 d e+2 a c^2 \left(a d^2-c e^2\right)-2 b^3 c d e+b^4 d^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}-\frac{(b d-c e) \left(-2 a c d+b^2 d-b c e\right) \log \left(a x^2+b x+c\right)}{2 a^2 \left(a d^2-e (b d-c e)\right)^2}-\frac{d^4}{e^3 (d+e x) \left(a d^2-e (b d-c e)\right)}-\frac{d^3 \log (d+e x) \left(2 a d^2-e (3 b d-4 c e)\right)}{e^3 \left(a d^2-e (b d-c e)\right)^2}+\frac{x}{a e^2}","-\frac{\left(-b^2 c \left(4 a d^2-c e^2\right)+6 a b c^2 d e+2 a c^2 \left(a d^2-c e^2\right)-2 b^3 c d e+b^4 d^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}-\frac{(b d-c e) \left(-2 a c d+b^2 d-b c e\right) \log \left(a x^2+b x+c\right)}{2 a^2 \left(a d^2-e (b d-c e)\right)^2}-\frac{d^4}{e^3 (d+e x) \left(a d^2-e (b d-c e)\right)}-\frac{d^3 \log (d+e x) \left(2 a d^2-e (3 b d-4 c e)\right)}{e^3 \left(a d^2-e (b d-c e)\right)^2}+\frac{x}{a e^2}",1,"x/(a*e^2) - d^4/(e^3*(a*d^2 - e*(b*d - c*e))*(d + e*x)) - ((b^4*d^2 - 2*b^3*c*d*e + 6*a*b*c^2*d*e + 2*a*c^2*(a*d^2 - c*e^2) - b^2*c*(4*a*d^2 - c*e^2))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(a^2*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) - (d^3*(2*a*d^2 - e*(3*b*d - 4*c*e))*Log[d + e*x])/(e^3*(a*d^2 - e*(b*d - c*e))^2) - ((b*d - c*e)*(b^2*d - 2*a*c*d - b*c*e)*Log[c + b*x + a*x^2])/(2*a^2*(a*d^2 - e*(b*d - c*e))^2)","A",7,6,25,0.2400,1,"{1569, 1628, 634, 618, 206, 628}"
72,1,246,0,0.3953464,"\int \frac{x}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) (d+e x)^2} \, dx","Int[x/((a + c/x^2 + b/x)*(d + e*x)^2),x]","\frac{\left(-b c \left(3 a d^2-c e^2\right)+4 a c^2 d e-2 b^2 c d e+b^3 d^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(-c \left(a d^2-c e^2\right)+b^2 d^2-2 b c d e\right) \log \left(a x^2+b x+c\right)}{2 a \left(a d^2-e (b d-c e)\right)^2}+\frac{d^3}{e^2 (d+e x) \left(a d^2-e (b d-c e)\right)}+\frac{d^2 \log (d+e x) \left(a d^2-e (2 b d-3 c e)\right)}{e^2 \left(a d^2-e (b d-c e)\right)^2}","\frac{\left(-b c \left(3 a d^2-c e^2\right)+4 a c^2 d e-2 b^2 c d e+b^3 d^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(-c \left(a d^2-c e^2\right)+b^2 d^2-2 b c d e\right) \log \left(a x^2+b x+c\right)}{2 a \left(a d^2-e (b d-c e)\right)^2}+\frac{d^3}{e^2 (d+e x) \left(a d^2-e (b d-c e)\right)}+\frac{d^2 \log (d+e x) \left(a d^2-e (2 b d-3 c e)\right)}{e^2 \left(a d^2-e (b d-c e)\right)^2}",1,"d^3/(e^2*(a*d^2 - e*(b*d - c*e))*(d + e*x)) + ((b^3*d^2 - 2*b^2*c*d*e + 4*a*c^2*d*e - b*c*(3*a*d^2 - c*e^2))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) + (d^2*(a*d^2 - e*(2*b*d - 3*c*e))*Log[d + e*x])/(e^2*(a*d^2 - e*(b*d - c*e))^2) + ((b^2*d^2 - 2*b*c*d*e - c*(a*d^2 - c*e^2))*Log[c + b*x + a*x^2])/(2*a*(a*d^2 - e*(b*d - c*e))^2)","A",7,6,23,0.2609,1,"{1569, 1628, 634, 618, 206, 628}"
73,1,194,0,0.3062834,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) (d+e x)^2} \, dx","Int[1/((a + c/x^2 + b/x)*(d + e*x)^2),x]","-\frac{\left(-2 c \left(a d^2-c e^2\right)+b^2 d^2-2 b c d e\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}-\frac{d^2}{e (d+e x) \left(a d^2-b d e+c e^2\right)}-\frac{d (b d-2 c e) \log \left(a x^2+b x+c\right)}{2 \left(a d^2-e (b d-c e)\right)^2}+\frac{d (b d-2 c e) \log (d+e x)}{\left(a d^2-e (b d-c e)\right)^2}","-\frac{\left(-2 c \left(a d^2-c e^2\right)+b^2 d^2-2 b c d e\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}-\frac{d^2}{e (d+e x) \left(a d^2-b d e+c e^2\right)}-\frac{d (b d-2 c e) \log \left(a x^2+b x+c\right)}{2 \left(a d^2-e (b d-c e)\right)^2}+\frac{d (b d-2 c e) \log (d+e x)}{\left(a d^2-e (b d-c e)\right)^2}",1,"-(d^2/(e*(a*d^2 - b*d*e + c*e^2)*(d + e*x))) - ((b^2*d^2 - 2*b*c*d*e - 2*c*(a*d^2 - c*e^2))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) + (d*(b*d - 2*c*e)*Log[d + e*x])/(a*d^2 - e*(b*d - c*e))^2 - (d*(b*d - 2*c*e)*Log[c + b*x + a*x^2])/(2*(a*d^2 - e*(b*d - c*e))^2)","A",7,6,22,0.2727,1,"{1445, 1628, 634, 618, 206, 628}"
74,1,183,0,0.2362793,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x (d+e x)^2} \, dx","Int[1/((a + c/x^2 + b/x)*x*(d + e*x)^2),x]","\frac{\left(a d (b d-4 c e)+b c e^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(a d^2-c e^2\right) \log \left(a x^2+b x+c\right)}{2 \left(a d^2-e (b d-c e)\right)^2}+\frac{d}{(d+e x) \left(a d^2-b d e+c e^2\right)}-\frac{\left(a d^2-c e^2\right) \log (d+e x)}{\left(a d^2-e (b d-c e)\right)^2}","\frac{\left(a d (b d-4 c e)+b c e^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(a d^2-c e^2\right) \log \left(a x^2+b x+c\right)}{2 \left(a d^2-e (b d-c e)\right)^2}+\frac{d}{(d+e x) \left(a d^2-b d e+c e^2\right)}-\frac{\left(a d^2-c e^2\right) \log (d+e x)}{\left(a d^2-e (b d-c e)\right)^2}",1,"d/((a*d^2 - b*d*e + c*e^2)*(d + e*x)) + ((b*c*e^2 + a*d*(b*d - 4*c*e))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) - ((a*d^2 - c*e^2)*Log[d + e*x])/(a*d^2 - e*(b*d - c*e))^2 + ((a*d^2 - c*e^2)*Log[c + b*x + a*x^2])/(2*(a*d^2 - e*(b*d - c*e))^2)","A",7,6,25,0.2400,1,"{1569, 800, 634, 618, 206, 628}"
75,1,189,0,0.3051993,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x^2 (d+e x)^2} \, dx","Int[1/((a + c/x^2 + b/x)*x^2*(d + e*x)^2),x]","-\frac{\left(2 a^2 d^2-2 a e (b d+c e)+b^2 e^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}-\frac{e}{(d+e x) \left(a d^2-b d e+c e^2\right)}-\frac{e (2 a d-b e) \log \left(a x^2+b x+c\right)}{2 \left(a d^2-e (b d-c e)\right)^2}+\frac{e (2 a d-b e) \log (d+e x)}{\left(a d^2-e (b d-c e)\right)^2}","-\frac{\left(2 a^2 d^2-2 a e (b d+c e)+b^2 e^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}-\frac{e}{(d+e x) \left(a d^2-b d e+c e^2\right)}-\frac{e (2 a d-b e) \log \left(a x^2+b x+c\right)}{2 \left(a d^2-e (b d-c e)\right)^2}+\frac{e (2 a d-b e) \log (d+e x)}{\left(a d^2-e (b d-c e)\right)^2}",1,"-(e/((a*d^2 - b*d*e + c*e^2)*(d + e*x))) - ((2*a^2*d^2 + b^2*e^2 - 2*a*e*(b*d + c*e))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) + (e*(2*a*d - b*e)*Log[d + e*x])/(a*d^2 - e*(b*d - c*e))^2 - (e*(2*a*d - b*e)*Log[c + b*x + a*x^2])/(2*(a*d^2 - e*(b*d - c*e))^2)","A",8,7,25,0.2800,1,"{1569, 709, 800, 634, 618, 206, 628}"
76,1,249,0,0.4086824,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x^3 (d+e x)^2} \, dx","Int[1/((a + c/x^2 + b/x)*x^3*(d + e*x)^2),x]","-\frac{\left(a^2 d^2-a e (2 b d+c e)+b^2 e^2\right) \log \left(a x^2+b x+c\right)}{2 c \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(a^2 d (b d+4 c e)-a b e (2 b d+3 c e)+b^3 e^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{e^2}{d (d+e x) \left(a d^2-e (b d-c e)\right)}-\frac{e^2 \log (d+e x) \left(3 a d^2-e (2 b d-c e)\right)}{d^2 \left(a d^2-e (b d-c e)\right)^2}+\frac{\log (x)}{c d^2}","-\frac{\left(a^2 d^2-a e (2 b d+c e)+b^2 e^2\right) \log \left(a x^2+b x+c\right)}{2 c \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(a^2 d (b d+4 c e)-a b e (2 b d+3 c e)+b^3 e^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{e^2}{d (d+e x) \left(a d^2-b d e+c e^2\right)}-\frac{e^2 \log (d+e x) \left(3 a d^2-e (2 b d-c e)\right)}{d^2 \left(a d^2-e (b d-c e)\right)^2}+\frac{\log (x)}{c d^2}",1,"e^2/(d*(a*d^2 - e*(b*d - c*e))*(d + e*x)) + ((b^3*e^2 - a*b*e*(2*b*d + 3*c*e) + a^2*d*(b*d + 4*c*e))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) + Log[x]/(c*d^2) - (e^2*(3*a*d^2 - e*(2*b*d - c*e))*Log[d + e*x])/(d^2*(a*d^2 - e*(b*d - c*e))^2) - ((a^2*d^2 + b^2*e^2 - a*e*(2*b*d + c*e))*Log[c + b*x + a*x^2])/(2*c*(a*d^2 - e*(b*d - c*e))^2)","A",7,6,25,0.2400,1,"{1569, 893, 634, 618, 206, 628}"
77,1,291,0,0.5632073,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x^4 (d+e x)^2} \, dx","Int[1/((a + c/x^2 + b/x)*x^4*(d + e*x)^2),x]","\frac{\left(-a^2 \left(b^2 d^2+6 b c d e+2 c^2 e^2\right)+2 a^3 c d^2+2 a b^2 e (b d+2 c e)+b^4 \left(-e^2\right)\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{(a d-b e) \left(a b d+2 a c e+b^2 (-e)\right) \log \left(a x^2+b x+c\right)}{2 c^2 \left(a d^2-e (b d-c e)\right)^2}-\frac{e^3}{d^2 (d+e x) \left(a d^2-e (b d-c e)\right)}+\frac{e^3 \log (d+e x) \left(4 a d^2-e (3 b d-2 c e)\right)}{d^3 \left(a d^2-e (b d-c e)\right)^2}-\frac{\log (x) (b d+2 c e)}{c^2 d^3}-\frac{1}{c d^2 x}","\frac{\left(-a^2 \left(b^2 d^2+6 b c d e+2 c^2 e^2\right)+2 a^3 c d^2+2 a b^2 e (b d+2 c e)+b^4 \left(-e^2\right)\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{(a d-b e) \left(a b d+2 a c e+b^2 (-e)\right) \log \left(a x^2+b x+c\right)}{2 c^2 \left(a d^2-e (b d-c e)\right)^2}-\frac{e^3}{d^2 (d+e x) \left(a d^2-e (b d-c e)\right)}+\frac{e^3 \log (d+e x) \left(4 a d^2-e (3 b d-2 c e)\right)}{d^3 \left(a d^2-e (b d-c e)\right)^2}-\frac{\log (x) (b d+2 c e)}{c^2 d^3}-\frac{1}{c d^2 x}",1,"-(1/(c*d^2*x)) - e^3/(d^2*(a*d^2 - e*(b*d - c*e))*(d + e*x)) + ((2*a^3*c*d^2 - b^4*e^2 + 2*a*b^2*e*(b*d + 2*c*e) - a^2*(b^2*d^2 + 6*b*c*d*e + 2*c^2*e^2))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) - ((b*d + 2*c*e)*Log[x])/(c^2*d^3) + (e^3*(4*a*d^2 - e*(3*b*d - 2*c*e))*Log[d + e*x])/(d^3*(a*d^2 - e*(b*d - c*e))^2) + ((a*d - b*e)*(a*b*d - b^2*e + 2*a*c*e)*Log[c + b*x + a*x^2])/(2*c^2*(a*d^2 - e*(b*d - c*e))^2)","A",7,6,25,0.2400,1,"{1569, 893, 634, 618, 206, 628}"
78,1,372,0,0.8510404,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right) x^5 (d+e x)^2} \, dx","Int[1/((a + c/x^2 + b/x)*x^5*(d + e*x)^2),x]","\frac{\left(-a^2 \left(b^2 d^2+4 b c d e+c^2 e^2\right)+a^3 c d^2+a b^2 e (2 b d+3 c e)+b^4 \left(-e^2\right)\right) \log \left(a x^2+b x+c\right)}{2 c^3 \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(a^2 b \left(b^2 d^2+8 b c d e+5 c^2 e^2\right)-a^3 c d (3 b d+4 c e)-a b^3 e (2 b d+5 c e)+b^5 e^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{\log (x) \left(-c \left(a d^2-3 c e^2\right)+b^2 d^2+2 b c d e\right)}{c^3 d^4}+\frac{e^4}{d^3 (d+e x) \left(a d^2-e (b d-c e)\right)}-\frac{e^4 \log (d+e x) \left(5 a d^2-e (4 b d-3 c e)\right)}{d^4 \left(a d^2-e (b d-c e)\right)^2}+\frac{b d+2 c e}{c^2 d^3 x}-\frac{1}{2 c d^2 x^2}","\frac{\left(-a^2 \left(b^2 d^2+4 b c d e+c^2 e^2\right)+a^3 c d^2+a b^2 e (2 b d+3 c e)+b^4 \left(-e^2\right)\right) \log \left(a x^2+b x+c\right)}{2 c^3 \left(a d^2-e (b d-c e)\right)^2}+\frac{\left(a^2 b \left(b^2 d^2+8 b c d e+5 c^2 e^2\right)-a^3 c d (3 b d+4 c e)-a b^3 e (2 b d+5 c e)+b^5 e^2\right) \tanh ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right)^2}+\frac{\log (x) \left(-c \left(a d^2-3 c e^2\right)+b^2 d^2+2 b c d e\right)}{c^3 d^4}+\frac{e^4}{d^3 (d+e x) \left(a d^2-e (b d-c e)\right)}-\frac{e^4 \log (d+e x) \left(5 a d^2-e (4 b d-3 c e)\right)}{d^4 \left(a d^2-e (b d-c e)\right)^2}+\frac{b d+2 c e}{c^2 d^3 x}-\frac{1}{2 c d^2 x^2}",1,"-1/(2*c*d^2*x^2) + (b*d + 2*c*e)/(c^2*d^3*x) + e^4/(d^3*(a*d^2 - e*(b*d - c*e))*(d + e*x)) + ((b^5*e^2 - a^3*c*d*(3*b*d + 4*c*e) - a*b^3*e*(2*b*d + 5*c*e) + a^2*b*(b^2*d^2 + 8*b*c*d*e + 5*c^2*e^2))*ArcTanh[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))^2) + ((b^2*d^2 + 2*b*c*d*e - c*(a*d^2 - 3*c*e^2))*Log[x])/(c^3*d^4) - (e^4*(5*a*d^2 - e*(4*b*d - 3*c*e))*Log[d + e*x])/(d^4*(a*d^2 - e*(b*d - c*e))^2) + ((a^3*c*d^2 - b^4*e^2 + a*b^2*e*(2*b*d + 3*c*e) - a^2*(b^2*d^2 + 4*b*c*d*e + c^2*e^2))*Log[c + b*x + a*x^2])/(2*c^3*(a*d^2 - e*(b*d - c*e))^2)","A",7,6,25,0.2400,1,"{1569, 893, 634, 618, 206, 628}"
79,1,981,0,6.1723848,"\int \sqrt{a+\frac{c}{x^2}+\frac{b}{x}} x^4 \sqrt{d+e x} \, dx","Int[Sqrt[a + c/x^2 + b/x]*x^4*Sqrt[d + e*x],x]","\frac{2}{11} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} x^5+\frac{2 (a d+b e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (d+e x)^{7/2} x}{99 a e^4}-\frac{2 \left(29 a^2 d^2+8 b^2 e^2+a e (19 b d-18 c e)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (d+e x)^{5/2} x}{693 a^2 e^4}+\frac{2 \left(233 a^3 d^3+4 a^2 e (18 b d-37 c e) d+48 b^3 e^3+a b e^2 (67 b d-157 c e)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (d+e x)^{3/2} x}{3465 a^3 e^4}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(128 a^5 d^5-4 a^4 e (14 b d-27 c e) d^3-a^3 e^2 \left(37 b^2 d^2-135 b c e d+156 c^2 e^2\right) d+128 b^5 e^5-8 a b^3 e^4 (7 b d+87 c e)-a^2 b e^3 \left(37 b^2 d^2-258 b c e d-771 c^2 e^2\right)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3465 a^5 e^5 \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \left(a x^2+b x+c\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right) \left(128 a^4 d^4+4 a^3 e (2 b d+3 c e) d^2-64 b^4 e^4-4 a b^2 e^3 (7 b d-69 c e)-3 a^2 e^2 \left(3 b^2 d^2-29 b c e d+50 c^2 e^2\right)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3465 a^5 e^5 \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{2 \left(187 a^4 d^4-4 a^3 e (2 b d+3 c e) d^2+64 b^4 e^4+4 a b^2 e^3 (7 b d-69 c e)+3 a^2 e^2 \left(3 b^2 d^2-29 b c e d+50 c^2 e^2\right)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} x}{3465 a^4 e^4}","\frac{2}{11} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} x^5+\frac{2 (a d+b e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (d+e x)^{7/2} x}{99 a e^4}-\frac{2 \left(29 a^2 d^2+8 b^2 e^2+a e (19 b d-18 c e)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (d+e x)^{5/2} x}{693 a^2 e^4}+\frac{2 \left(233 a^3 d^3+4 a^2 e (18 b d-37 c e) d+48 b^3 e^3+a b e^2 (67 b d-157 c e)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (d+e x)^{3/2} x}{3465 a^3 e^4}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(128 a^5 d^5-4 a^4 e (14 b d-27 c e) d^3-a^3 e^2 \left(37 b^2 d^2-135 b c e d+156 c^2 e^2\right) d+128 b^5 e^5-8 a b^3 e^4 (7 b d+87 c e)-a^2 b e^3 \left(37 b^2 d^2-258 b c e d-771 c^2 e^2\right)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3465 a^5 e^5 \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \left(a x^2+b x+c\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(a d^2-e (b d-c e)\right) \left(128 a^4 d^4+4 a^3 e (2 b d+3 c e) d^2-64 b^4 e^4-4 a b^2 e^3 (7 b d-69 c e)-3 a^2 e^2 \left(3 b^2 d^2-29 b c e d+50 c^2 e^2\right)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3465 a^5 e^5 \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{2 \left(187 a^4 d^4-4 a^3 e (2 b d+3 c e) d^2+64 b^4 e^4+4 a b^2 e^3 (7 b d-69 c e)+3 a^2 e^2 \left(3 b^2 d^2-29 b c e d+50 c^2 e^2\right)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} x}{3465 a^4 e^4}",1,"(-2*(187*a^4*d^4 + 64*b^4*e^4 + 4*a*b^2*e^3*(7*b*d - 69*c*e) - 4*a^3*d^2*e*(2*b*d + 3*c*e) + 3*a^2*e^2*(3*b^2*d^2 - 29*b*c*d*e + 50*c^2*e^2))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x])/(3465*a^4*e^4) + (2*Sqrt[a + c/x^2 + b/x]*x^5*Sqrt[d + e*x])/11 + (2*(233*a^3*d^3 + 48*b^3*e^3 + a*b*e^2*(67*b*d - 157*c*e) + 4*a^2*d*e*(18*b*d - 37*c*e))*Sqrt[a + c/x^2 + b/x]*x*(d + e*x)^(3/2))/(3465*a^3*e^4) - (2*(29*a^2*d^2 + 8*b^2*e^2 + a*e*(19*b*d - 18*c*e))*Sqrt[a + c/x^2 + b/x]*x*(d + e*x)^(5/2))/(693*a^2*e^4) + (2*(a*d + b*e)*Sqrt[a + c/x^2 + b/x]*x*(d + e*x)^(7/2))/(99*a*e^4) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*a^5*d^5 + 128*b^5*e^5 - 4*a^4*d^3*e*(14*b*d - 27*c*e) - 8*a*b^3*e^4*(7*b*d + 87*c*e) - a^2*b*e^3*(37*b^2*d^2 - 258*b*c*d*e - 771*c^2*e^2) - a^3*d*e^2*(37*b^2*d^2 - 135*b*c*d*e + 156*c^2*e^2))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3465*a^5*e^5*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*(c + b*x + a*x^2)) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(a*d^2 - e*(b*d - c*e))*(128*a^4*d^4 - 64*b^4*e^4 - 4*a*b^2*e^3*(7*b*d - 69*c*e) + 4*a^3*d^2*e*(2*b*d + 3*c*e) - 3*a^2*e^2*(3*b^2*d^2 - 29*b*c*d*e + 50*c^2*e^2))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3465*a^5*e^5*Sqrt[d + e*x]*(c + b*x + a*x^2))","A",11,7,29,0.2414,1,"{1573, 918, 1653, 843, 718, 424, 419}"
80,1,778,0,2.349196,"\int \sqrt{a+\frac{c}{x^2}+\frac{b}{x}} x^3 \sqrt{d+e x} \, dx","Int[Sqrt[a + c/x^2 + b/x]*x^3*Sqrt[d + e*x],x]","-\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(-3 a^2 e^2 \left(b^2 d^2-5 b c d e-7 c^2 e^2\right)-a^3 d^2 e (4 b d-9 c e)+8 a^4 d^4-4 a b^2 e^3 (b d+9 c e)+8 b^4 e^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 a^4 e^4 \left(a x^2+b x+c\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{4 x (d+e x)^{3/2} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \left(8 a^2 d^2+a e (4 b d-7 c e)+3 b^2 e^2\right)}{315 a^2 e^3}+\frac{2 x \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \left(-6 a^2 c d e^2+19 a^3 d^3+3 a b e^2 (b d-9 c e)+8 b^3 e^3\right)}{315 a^3 e^3}+\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(6 a^2 c d e^2+16 a^3 d^3-3 a b e^2 (b d-9 c e)-8 b^3 e^3\right) \left(a d^2-e (b d-c e)\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 a^4 e^4 \sqrt{d+e x} \left(a x^2+b x+c\right)}+\frac{2 x (d+e x)^{5/2} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (a d+b e)}{63 a e^3}+\frac{2}{9} x^4 \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}","-\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(-3 a^2 e^2 \left(b^2 d^2-5 b c d e-7 c^2 e^2\right)-a^3 d^2 e (4 b d-9 c e)+8 a^4 d^4-4 a b^2 e^3 (b d+9 c e)+8 b^4 e^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 a^4 e^4 \left(a x^2+b x+c\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{4 x (d+e x)^{3/2} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \left(8 a^2 d^2+a e (4 b d-7 c e)+3 b^2 e^2\right)}{315 a^2 e^3}+\frac{2 x \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \left(-6 a^2 c d e^2+19 a^3 d^3+3 a b e^2 (b d-9 c e)+8 b^3 e^3\right)}{315 a^3 e^3}+\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(6 a^2 c d e^2+16 a^3 d^3-3 a b e^2 (b d-9 c e)-8 b^3 e^3\right) \left(a d^2-e (b d-c e)\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 a^4 e^4 \sqrt{d+e x} \left(a x^2+b x+c\right)}+\frac{2 x (d+e x)^{5/2} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (a d+b e)}{63 a e^3}+\frac{2}{9} x^4 \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}",1,"(2*(19*a^3*d^3 - 6*a^2*c*d*e^2 + 8*b^3*e^3 + 3*a*b*e^2*(b*d - 9*c*e))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x])/(315*a^3*e^3) + (2*Sqrt[a + c/x^2 + b/x]*x^4*Sqrt[d + e*x])/9 - (4*(8*a^2*d^2 + 3*b^2*e^2 + a*e*(4*b*d - 7*c*e))*Sqrt[a + c/x^2 + b/x]*x*(d + e*x)^(3/2))/(315*a^2*e^3) + (2*(a*d + b*e)*Sqrt[a + c/x^2 + b/x]*x*(d + e*x)^(5/2))/(63*a*e^3) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(8*a^4*d^4 + 8*b^4*e^4 - a^3*d^2*e*(4*b*d - 9*c*e) - 4*a*b^2*e^3*(b*d + 9*c*e) - 3*a^2*e^2*(b^2*d^2 - 5*b*c*d*e - 7*c^2*e^2))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*a^4*e^4*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*(c + b*x + a*x^2)) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*a^3*d^3 + 6*a^2*c*d*e^2 - 8*b^3*e^3 - 3*a*b*e^2*(b*d - 9*c*e))*(a*d^2 - e*(b*d - c*e))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*a^4*e^4*Sqrt[d + e*x]*(c + b*x + a*x^2))","A",10,7,29,0.2414,1,"{1573, 918, 1653, 843, 718, 424, 419}"
81,1,636,0,0.9930444,"\int \sqrt{a+\frac{c}{x^2}+\frac{b}{x}} x^2 \sqrt{d+e x} \, dx","Int[Sqrt[a + c/x^2 + b/x]*x^2*Sqrt[d + e*x],x]","-\frac{2 x \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \left(4 a^2 d^2-a e (2 b d-5 c e)-3 a e x (a d-4 b e)+4 b^2 e^2\right)}{105 a^2 e^2}-\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(8 a^2 d^2-a e (b d-10 c e)-4 b^2 e^2\right) \left(a d^2-e (b d-c e)\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 a^3 e^3 \sqrt{d+e x} \left(a x^2+b x+c\right)}+\frac{\sqrt{2} x \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(-a^2 d e (5 b d-16 c e)+8 a^3 d^3-a b e^2 (5 b d+29 c e)+8 b^3 e^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 a^3 e^3 \left(a x^2+b x+c\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 x \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \left(a x^2+b x+c\right)}{7 a}","-\frac{2 x \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \left(4 a^2 d^2-a e (2 b d-5 c e)-3 a e x (a d-4 b e)+4 b^2 e^2\right)}{105 a^2 e^2}-\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(8 a^2 d^2-a e (b d-10 c e)-4 b^2 e^2\right) \left(a d^2-e (b d-c e)\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 a^3 e^3 \sqrt{d+e x} \left(a x^2+b x+c\right)}+\frac{\sqrt{2} x \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(-a^2 d e (5 b d-16 c e)+8 a^3 d^3-a b e^2 (5 b d+29 c e)+8 b^3 e^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 a^3 e^3 \left(a x^2+b x+c\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 x \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \left(a x^2+b x+c\right)}{7 a}",1,"(-2*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*(4*a^2*d^2 + 4*b^2*e^2 - a*e*(2*b*d - 5*c*e) - 3*a*e*(a*d - 4*b*e)*x))/(105*a^2*e^2) + (2*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*(c + b*x + a*x^2))/(7*a) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(8*a^3*d^3 + 8*b^3*e^3 - a^2*d*e*(5*b*d - 16*c*e) - a*b*e^2*(5*b*d + 29*c*e))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*a^3*e^3*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*(c + b*x + a*x^2)) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(8*a^2*d^2 - 4*b^2*e^2 - a*e*(b*d - 10*c*e))*(a*d^2 - e*(b*d - c*e))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*a^3*e^3*Sqrt[d + e*x]*(c + b*x + a*x^2))","A",8,7,29,0.2414,1,"{1573, 832, 814, 843, 718, 424, 419}"
82,1,550,0,0.6554542,"\int \sqrt{a+\frac{c}{x^2}+\frac{b}{x}} x \sqrt{d+e x} \, dx","Int[Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x],x]","\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} (2 a d-b e) \left(a d^2-e (b d-c e)\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 a^2 e^2 \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(a^2 d^2-a e (b d+3 c e)+b^2 e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 a^2 e^2 \left(a x^2+b x+c\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 x (d+e x)^{3/2} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{5 e}-\frac{2 x \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (2 a d-b e)}{15 a e}","\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} (2 a d-b e) \left(a d^2-e (b d-c e)\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 a^2 e^2 \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{2 \sqrt{2} x \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} \left(a^2 d^2-a e (b d+3 c e)+b^2 e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 a^2 e^2 \left(a x^2+b x+c\right) \sqrt{\frac{a (d+e x)}{2 a d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 x (d+e x)^{3/2} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{5 e}-\frac{2 x \sqrt{d+e x} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} (2 a d-b e)}{15 a e}",1,"(-2*(2*a*d - b*e)*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x])/(15*a*e) + (2*Sqrt[a + c/x^2 + b/x]*x*(d + e*x)^(3/2))/(5*e) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(a^2*d^2 + b^2*e^2 - a*e*(b*d + 3*c*e))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*a^2*e^2*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*(c + b*x + a*x^2)) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*a*d - b*e)*(a*d^2 - e*(b*d - c*e))*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*a^2*e^2*Sqrt[d + e*x]*(c + b*x + a*x^2))","A",8,7,27,0.2593,1,"{1573, 734, 832, 843, 718, 424, 419}"
83,1,955,0,3.3127232,"\int \sqrt{a+\frac{c}{x^2}+\frac{b}{x}} \sqrt{d+e x} \, dx","Int[Sqrt[a + c/x^2 + b/x]*Sqrt[d + e*x],x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} (a d+b e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3 a e \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \left(a x^2+b x+c\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} d (a d+b e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3 a e \sqrt{d+e x} \left(a x^2+b x+c\right)}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} (b d+c e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3 a \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{\sqrt{2} c \sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \Pi \left(\frac{2 a d-b e+\sqrt{b^2-4 a c} e}{2 a d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{d+e x}}{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 a d}{e}}{b+\sqrt{b^2-4 a c}-\frac{2 a d}{e}}\right) x}{\sqrt{a} \left(a x^2+b x+c\right)}+\frac{2}{3} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} x","\frac{\sqrt{2} \sqrt{b^2-4 a c} (a d+b e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3 a e \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \left(a x^2+b x+c\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} d (a d+b e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3 a e \sqrt{d+e x} \left(a x^2+b x+c\right)}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} (b d+c e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) x}{3 a \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{\sqrt{2} c \sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \Pi \left(\frac{2 a d-b e+\sqrt{b^2-4 a c} e}{2 a d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{d+e x}}{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 a d}{e}}{b+\sqrt{b^2-4 a c}-\frac{2 a d}{e}}\right) x}{\sqrt{a} \left(a x^2+b x+c\right)}+\frac{2}{3} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} x",1,"(2*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x])/3 + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(a*d + b*e)*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*a*e*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*(c + b*x + a*x^2)) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*d*(a*d + b*e)*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*a*e*Sqrt[d + e*x]*(c + b*x + a*x^2)) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(b*d + c*e)*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*a*Sqrt[d + e*x]*(c + b*x + a*x^2)) - (Sqrt[2]*c*Sqrt[2*a*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[a + c/x^2 + b/x]*x*Sqrt[1 - (2*a*(d + e*x))/(2*a*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*EllipticPi[(2*a*d - b*e + Sqrt[b^2 - 4*a*c]*e)/(2*a*d), ArcSin[(Sqrt[2]*Sqrt[a]*Sqrt[d + e*x])/Sqrt[2*a*d - (b - Sqrt[b^2 - 4*a*c])*e]], (b - Sqrt[b^2 - 4*a*c] - (2*a*d)/e)/(b + Sqrt[b^2 - 4*a*c] - (2*a*d)/e)])/(Sqrt[a]*(c + b*x + a*x^2))","A",16,11,26,0.4231,1,"{1449, 918, 6742, 718, 419, 934, 169, 538, 537, 843, 424}"
84,1,929,0,2.7248655,"\int \frac{\sqrt{a+\frac{c}{x^2}+\frac{b}{x}} \sqrt{d+e x}}{x} \, dx","Int[(Sqrt[a + c/x^2 + b/x]*Sqrt[d + e*x])/x,x]","\frac{3 \sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{d+e x} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{2} \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \left(a x^2+b x+c\right)}-\frac{3 \sqrt{2} \sqrt{b^2-4 a c} d \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{d+e x} \left(a x^2+b x+c\right)}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (a d+b e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{a \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{(b d+c e) \sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \Pi \left(\frac{2 a d-b e+\sqrt{b^2-4 a c} e}{2 a d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{d+e x}}{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 a d}{e}}{b+\sqrt{b^2-4 a c}-\frac{2 a d}{e}}\right)}{\sqrt{2} \sqrt{a} d \left(a x^2+b x+c\right)}-\sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x}","\frac{3 \sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{d+e x} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{2} \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \left(a x^2+b x+c\right)}-\frac{3 \sqrt{2} \sqrt{b^2-4 a c} d \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{d+e x} \left(a x^2+b x+c\right)}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (a d+b e) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{a \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{(b d+c e) \sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \Pi \left(\frac{2 a d-b e+\sqrt{b^2-4 a c} e}{2 a d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{d+e x}}{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 a d}{e}}{b+\sqrt{b^2-4 a c}-\frac{2 a d}{e}}\right)}{\sqrt{2} \sqrt{a} d \left(a x^2+b x+c\right)}-\sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x}",1,"-(Sqrt[a + c/x^2 + b/x]*Sqrt[d + e*x]) + (3*Sqrt[b^2 - 4*a*c]*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[2]*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*(c + b*x + a*x^2)) - (3*Sqrt[2]*Sqrt[b^2 - 4*a*c]*d*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[d + e*x]*(c + b*x + a*x^2)) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(a*d + b*e)*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(a*Sqrt[d + e*x]*(c + b*x + a*x^2)) - ((b*d + c*e)*Sqrt[2*a*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[a + c/x^2 + b/x]*x*Sqrt[1 - (2*a*(d + e*x))/(2*a*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*EllipticPi[(2*a*d - b*e + Sqrt[b^2 - 4*a*c]*e)/(2*a*d), ArcSin[(Sqrt[2]*Sqrt[a]*Sqrt[d + e*x])/Sqrt[2*a*d - (b - Sqrt[b^2 - 4*a*c])*e]], (b - Sqrt[b^2 - 4*a*c] - (2*a*d)/e)/(b + Sqrt[b^2 - 4*a*c] - (2*a*d)/e)])/(Sqrt[2]*Sqrt[a]*d*(c + b*x + a*x^2))","A",16,11,29,0.3793,1,"{1573, 916, 6742, 718, 419, 934, 169, 538, 537, 843, 424}"
85,1,1287,0,5.3023912,"\int \frac{\sqrt{a+\frac{c}{x^2}+\frac{b}{x}} \sqrt{d+e x}}{x^2} \, dx","Int[(Sqrt[a + c/x^2 + b/x]*Sqrt[d + e*x])/x^2,x]","\frac{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \Pi \left(\frac{2 a d-b e+\sqrt{b^2-4 a c} e}{2 a d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{d+e x}}{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 a d}{e}}{b+\sqrt{b^2-4 a c}-\frac{2 a d}{e}}\right) (b d+c e)^2}{4 \sqrt{2} \sqrt{a} c d^2 \left(a x^2+b x+c\right)}+\frac{\sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{d+e x} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) (b d+c e)}{4 \sqrt{2} c d \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \left(a x^2+b x+c\right)}-\frac{\sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) (b d+c e)}{2 \sqrt{2} c \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{\sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} (b d+c e)}{4 c d}+\frac{3 \sqrt{b^2-4 a c} e \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{2} \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{(a d+b e) \sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \Pi \left(\frac{2 a d-b e+\sqrt{b^2-4 a c} e}{2 a d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{d+e x}}{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 a d}{e}}{b+\sqrt{b^2-4 a c}-\frac{2 a d}{e}}\right)}{\sqrt{2} \sqrt{a} d \left(a x^2+b x+c\right)}-\frac{\sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x}}{2 x}","\frac{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \Pi \left(\frac{2 a d-b e+\sqrt{b^2-4 a c} e}{2 a d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{d+e x}}{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 a d}{e}}{b+\sqrt{b^2-4 a c}-\frac{2 a d}{e}}\right) (b d+c e)^2}{4 \sqrt{2} \sqrt{a} c d^2 \left(a x^2+b x+c\right)}+\frac{\sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{d+e x} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) (b d+c e)}{4 \sqrt{2} c d \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \left(a x^2+b x+c\right)}-\frac{\sqrt{b^2-4 a c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) (b d+c e)}{2 \sqrt{2} c \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{\sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x} (b d+c e)}{4 c d}+\frac{3 \sqrt{b^2-4 a c} e \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{\frac{a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{a \left(a x^2+b x+c\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 a x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{2} \sqrt{d+e x} \left(a x^2+b x+c\right)}-\frac{(a d+b e) \sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} x \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}} \sqrt{1-\frac{2 a (d+e x)}{2 a d-\left(b+\sqrt{b^2-4 a c}\right) e}} \Pi \left(\frac{2 a d-b e+\sqrt{b^2-4 a c} e}{2 a d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{d+e x}}{\sqrt{2 a d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 a d}{e}}{b+\sqrt{b^2-4 a c}-\frac{2 a d}{e}}\right)}{\sqrt{2} \sqrt{a} d \left(a x^2+b x+c\right)}-\frac{\sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{d+e x}}{2 x}",1,"-((b*d + c*e)*Sqrt[a + c/x^2 + b/x]*Sqrt[d + e*x])/(4*c*d) - (Sqrt[a + c/x^2 + b/x]*Sqrt[d + e*x])/(2*x) + (Sqrt[b^2 - 4*a*c]*(b*d + c*e)*Sqrt[a + c/x^2 + b/x]*x*Sqrt[d + e*x]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(4*Sqrt[2]*c*d*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*(c + b*x + a*x^2)) + (3*Sqrt[b^2 - 4*a*c]*e*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[2]*Sqrt[d + e*x]*(c + b*x + a*x^2)) - (Sqrt[b^2 - 4*a*c]*(b*d + c*e)*Sqrt[a + c/x^2 + b/x]*x*Sqrt[(a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((a*(c + b*x + a*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*a*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(2*Sqrt[2]*c*Sqrt[d + e*x]*(c + b*x + a*x^2)) - ((a*d + b*e)*Sqrt[2*a*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[a + c/x^2 + b/x]*x*Sqrt[1 - (2*a*(d + e*x))/(2*a*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*EllipticPi[(2*a*d - b*e + Sqrt[b^2 - 4*a*c]*e)/(2*a*d), ArcSin[(Sqrt[2]*Sqrt[a]*Sqrt[d + e*x])/Sqrt[2*a*d - (b - Sqrt[b^2 - 4*a*c])*e]], (b - Sqrt[b^2 - 4*a*c] - (2*a*d)/e)/(b + Sqrt[b^2 - 4*a*c] - (2*a*d)/e)])/(Sqrt[2]*Sqrt[a]*d*(c + b*x + a*x^2)) + ((b*d + c*e)^2*Sqrt[2*a*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[a + c/x^2 + b/x]*x*Sqrt[1 - (2*a*(d + e*x))/(2*a*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*a*(d + e*x))/(2*a*d - (b + Sqrt[b^2 - 4*a*c])*e)]*EllipticPi[(2*a*d - b*e + Sqrt[b^2 - 4*a*c]*e)/(2*a*d), ArcSin[(Sqrt[2]*Sqrt[a]*Sqrt[d + e*x])/Sqrt[2*a*d - (b - Sqrt[b^2 - 4*a*c])*e]], (b - Sqrt[b^2 - 4*a*c] - (2*a*d)/e)/(b + Sqrt[b^2 - 4*a*c] - (2*a*d)/e)])/(4*Sqrt[2]*Sqrt[a]*c*d^2*(c + b*x + a*x^2))","A",24,12,29,0.4138,1,"{1573, 916, 6742, 718, 419, 939, 934, 169, 538, 537, 843, 424}"
86,0,0,0,0.0186216,"\int (f x)^m \left(d+e x^n\right)^q \left(a+c x^{2 n}\right)^p \, dx","Int[(f*x)^m*(d + e*x^n)^q*(a + c*x^(2*n))^p,x]","\int (f x)^m \left(d+e x^n\right)^q \left(a+c x^{2 n}\right)^p \, dx","\text{Int}\left((f x)^m \left(a+c x^{2 n}\right)^p \left(d+e x^n\right)^q,x\right)",0,"Defer[Int][(f*x)^m*(d + e*x^n)^q*(a + c*x^(2*n))^p, x]","A",0,0,0,0,-1,"{}"
87,1,358,0,0.2369082,"\int (f x)^m \left(d+e x^n\right)^3 \left(a+c x^{2 n}\right)^p \, dx","Int[(f*x)^m*(d + e*x^n)^3*(a + c*x^(2*n))^p,x]","\frac{3 d^2 e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+n+1}{2 n},-p;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+n+1}+\frac{d^3 (f x)^{m+1} \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2 n},-p;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a}\right)}{f (m+1)}+\frac{3 d e^2 x^{2 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2 n+1}{2 n},-p;\frac{m+4 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+2 n+1}+\frac{e^3 x^{3 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+3 n+1}{2 n},-p;\frac{m+5 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+3 n+1}","\frac{3 d^2 e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+n+1}{2 n},-p;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+n+1}+\frac{d^3 (f x)^{m+1} \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2 n},-p;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a}\right)}{f (m+1)}+\frac{3 d e^2 x^{2 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2 n+1}{2 n},-p;\frac{m+4 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+2 n+1}+\frac{e^3 x^{3 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+3 n+1}{2 n},-p;\frac{m+5 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+3 n+1}",1,"(d^3*(f*x)^(1 + m)*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m)/(2*n), -p, 1 + (1 + m)/(2*n), -((c*x^(2*n))/a)])/(f*(1 + m)*(1 + (c*x^(2*n))/a)^p) + (3*d^2*e*x^(1 + n)*(f*x)^m*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m + n)/(2*n), -p, (1 + m + 3*n)/(2*n), -((c*x^(2*n))/a)])/((1 + m + n)*(1 + (c*x^(2*n))/a)^p) + (3*d*e^2*x^(1 + 2*n)*(f*x)^m*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m + 2*n)/(2*n), -p, (1 + m + 4*n)/(2*n), -((c*x^(2*n))/a)])/((1 + m + 2*n)*(1 + (c*x^(2*n))/a)^p) + (e^3*x^(1 + 3*n)*(f*x)^m*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m + 3*n)/(2*n), -p, (1 + m + 5*n)/(2*n), -((c*x^(2*n))/a)])/((1 + m + 3*n)*(1 + (c*x^(2*n))/a)^p)","A",13,4,26,0.1538,1,"{1561, 365, 364, 20}"
88,1,262,0,0.1595327,"\int (f x)^m \left(d+e x^n\right)^2 \left(a+c x^{2 n}\right)^p \, dx","Int[(f*x)^m*(d + e*x^n)^2*(a + c*x^(2*n))^p,x]","\frac{d^2 (f x)^{m+1} \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2 n},-p;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a}\right)}{f (m+1)}+\frac{2 d e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+n+1}{2 n},-p;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+n+1}+\frac{e^2 x^{2 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2 n+1}{2 n},-p;\frac{m+4 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+2 n+1}","\frac{d^2 (f x)^{m+1} \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2 n},-p;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a}\right)}{f (m+1)}+\frac{2 d e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+n+1}{2 n},-p;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+n+1}+\frac{e^2 x^{2 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2 n+1}{2 n},-p;\frac{m+4 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+2 n+1}",1,"(d^2*(f*x)^(1 + m)*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m)/(2*n), -p, 1 + (1 + m)/(2*n), -((c*x^(2*n))/a)])/(f*(1 + m)*(1 + (c*x^(2*n))/a)^p) + (2*d*e*x^(1 + n)*(f*x)^m*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m + n)/(2*n), -p, (1 + m + 3*n)/(2*n), -((c*x^(2*n))/a)])/((1 + m + n)*(1 + (c*x^(2*n))/a)^p) + (e^2*x^(1 + 2*n)*(f*x)^m*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m + 2*n)/(2*n), -p, (1 + m + 4*n)/(2*n), -((c*x^(2*n))/a)])/((1 + m + 2*n)*(1 + (c*x^(2*n))/a)^p)","A",10,4,26,0.1538,1,"{1561, 365, 364, 20}"
89,1,166,0,0.0946427,"\int (f x)^m \left(d+e x^n\right) \left(a+c x^{2 n}\right)^p \, dx","Int[(f*x)^m*(d + e*x^n)*(a + c*x^(2*n))^p,x]","\frac{d (f x)^{m+1} \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2 n},-p;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a}\right)}{f (m+1)}+\frac{e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+n+1}{2 n},-p;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+n+1}","\frac{d (f x)^{m+1} \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2 n},-p;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a}\right)}{f (m+1)}+\frac{e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+n+1}{2 n},-p;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a}\right)}{m+n+1}",1,"(d*(f*x)^(1 + m)*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m)/(2*n), -p, 1 + (1 + m)/(2*n), -((c*x^(2*n))/a)])/(f*(1 + m)*(1 + (c*x^(2*n))/a)^p) + (e*x^(1 + n)*(f*x)^m*(a + c*x^(2*n))^p*Hypergeometric2F1[(1 + m + n)/(2*n), -p, (1 + m + 3*n)/(2*n), -((c*x^(2*n))/a)])/((1 + m + n)*(1 + (c*x^(2*n))/a)^p)","A",7,4,24,0.1667,1,"{1561, 365, 364, 20}"
90,1,194,0,0.2239105,"\int \frac{(f x)^m \left(a+c x^{2 n}\right)^p}{d+e x^n} \, dx","Int[((f*x)^m*(a + c*x^(2*n))^p)/(d + e*x^n),x]","\frac{x (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2 n};-p,1;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d (m+1)}-\frac{e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+n+1}{2 n};-p,1;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^2 (m+n+1)}","\frac{x (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2 n};-p,1;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d (m+1)}-\frac{e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+n+1}{2 n};-p,1;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^2 (m+n+1)}",1,"(x*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m)/(2*n), -p, 1, 1 + (1 + m)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d*(1 + m)*(1 + (c*x^(2*n))/a)^p) - (e*x^(1 + n)*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m + n)/(2*n), -p, 1, (1 + m + 3*n)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d^2*(1 + m + n)*(1 + (c*x^(2*n))/a)^p)","A",6,3,26,0.1154,1,"{1562, 511, 510}"
91,1,302,0,0.3325531,"\int \frac{(f x)^m \left(a+c x^{2 n}\right)^p}{\left(d+e x^n\right)^2} \, dx","Int[((f*x)^m*(a + c*x^(2*n))^p)/(d + e*x^n)^2,x]","\frac{x (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2 n};-p,2;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^2 (m+1)}-\frac{2 e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+n+1}{2 n};-p,2;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^3 (m+n+1)}+\frac{e^2 x^{2 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+2 n+1}{2 n};-p,2;\frac{m+4 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^4 (m+2 n+1)}","\frac{x (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2 n};-p,2;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^2 (m+1)}-\frac{2 e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+n+1}{2 n};-p,2;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^3 (m+n+1)}+\frac{e^2 x^{2 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+2 n+1}{2 n};-p,2;\frac{m+4 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^4 (m+2 n+1)}",1,"(x*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m)/(2*n), -p, 2, 1 + (1 + m)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d^2*(1 + m)*(1 + (c*x^(2*n))/a)^p) - (2*e*x^(1 + n)*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m + n)/(2*n), -p, 2, (1 + m + 3*n)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d^3*(1 + m + n)*(1 + (c*x^(2*n))/a)^p) + (e^2*x^(1 + 2*n)*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m + 2*n)/(2*n), -p, 2, (1 + m + 4*n)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d^4*(1 + m + 2*n)*(1 + (c*x^(2*n))/a)^p)","A",8,3,26,0.1154,1,"{1562, 511, 510}"
92,1,412,0,0.4494586,"\int \frac{(f x)^m \left(a+c x^{2 n}\right)^p}{\left(d+e x^n\right)^3} \, dx","Int[((f*x)^m*(a + c*x^(2*n))^p)/(d + e*x^n)^3,x]","\frac{x (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2 n};-p,3;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^3 (m+1)}-\frac{3 e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+n+1}{2 n};-p,3;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^4 (m+n+1)}+\frac{3 e^2 x^{2 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+2 n+1}{2 n};-p,3;\frac{m+4 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^5 (m+2 n+1)}-\frac{e^3 x^{3 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+3 n+1}{2 n};-p,3;\frac{m+5 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^6 (m+3 n+1)}","\frac{x (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2 n};-p,3;\frac{m+1}{2 n}+1;-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^3 (m+1)}-\frac{3 e x^{n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+n+1}{2 n};-p,3;\frac{m+3 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^4 (m+n+1)}+\frac{3 e^2 x^{2 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+2 n+1}{2 n};-p,3;\frac{m+4 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^5 (m+2 n+1)}-\frac{e^3 x^{3 n+1} (f x)^m \left(a+c x^{2 n}\right)^p \left(\frac{c x^{2 n}}{a}+1\right)^{-p} F_1\left(\frac{m+3 n+1}{2 n};-p,3;\frac{m+5 n+1}{2 n};-\frac{c x^{2 n}}{a},\frac{e^2 x^{2 n}}{d^2}\right)}{d^6 (m+3 n+1)}",1,"(x*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m)/(2*n), -p, 3, 1 + (1 + m)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d^3*(1 + m)*(1 + (c*x^(2*n))/a)^p) - (3*e*x^(1 + n)*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m + n)/(2*n), -p, 3, (1 + m + 3*n)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d^4*(1 + m + n)*(1 + (c*x^(2*n))/a)^p) + (3*e^2*x^(1 + 2*n)*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m + 2*n)/(2*n), -p, 3, (1 + m + 4*n)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d^5*(1 + m + 2*n)*(1 + (c*x^(2*n))/a)^p) - (e^3*x^(1 + 3*n)*(f*x)^m*(a + c*x^(2*n))^p*AppellF1[(1 + m + 3*n)/(2*n), -p, 3, (1 + m + 5*n)/(2*n), -((c*x^(2*n))/a), (e^2*x^(2*n))/d^2])/(d^6*(1 + m + 3*n)*(1 + (c*x^(2*n))/a)^p)","A",10,3,26,0.1154,1,"{1562, 511, 510}"
93,1,16,0,0.0603052,"\int (b+2 c x) \left(a+b x+c x^2\right)^{13} \, dx","Int[(b + 2*c*x)*(a + b*x + c*x^2)^13,x]","\frac{1}{14} \left(a+b x+c x^2\right)^{14}","\frac{1}{14} \left(a+b x+c x^2\right)^{14}",1,"(a + b*x + c*x^2)^14/14","A",1,1,19,0.05263,1,"{629}"
94,1,18,0,0.3292368,"\int x \left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{13} \, dx","Int[x*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^13,x]","\frac{1}{28} \left(a+b x^2+c x^4\right)^{14}","\frac{1}{28} \left(a+b x^2+c x^4\right)^{14}",1,"(a + b*x^2 + c*x^4)^14/28","A",2,2,24,0.08333,1,"{1247, 629}"
95,1,18,0,0.3020017,"\int x^2 \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{13} \, dx","Int[x^2*(b + 2*c*x^3)*(a + b*x^3 + c*x^6)^13,x]","\frac{1}{42} \left(a+b x^3+c x^6\right)^{14}","\frac{1}{42} \left(a+b x^3+c x^6\right)^{14}",1,"(a + b*x^3 + c*x^6)^14/42","A",2,2,26,0.07692,1,"{1468, 629}"
96,1,23,0,0.0559981,"\int x^{-1+n} \left(b+2 c x^n\right) \left(a+b x^n+c x^{2 n}\right)^{13} \, dx","Int[x^(-1 + n)*(b + 2*c*x^n)*(a + b*x^n + c*x^(2*n))^13,x]","\frac{\left(a+b x^n+c x^{2 n}\right)^{14}}{14 n}","\frac{\left(a+b x^n+c x^{2 n}\right)^{14}}{14 n}",1,"(a + b*x^n + c*x^(2*n))^14/(14*n)","A",2,2,30,0.06667,1,"{1468, 629}"
97,1,18,0,0.0687475,"\int (b+2 c x) \left(-a+b x+c x^2\right)^{13} \, dx","Int[(b + 2*c*x)*(-a + b*x + c*x^2)^13,x]","\frac{1}{14} \left(a-b x-c x^2\right)^{14}","\frac{1}{14} \left(a-b x-c x^2\right)^{14}",1,"(a - b*x - c*x^2)^14/14","A",1,1,21,0.04762,1,"{629}"
98,1,20,0,0.3217101,"\int x \left(b+2 c x^2\right) \left(-a+b x^2+c x^4\right)^{13} \, dx","Int[x*(b + 2*c*x^2)*(-a + b*x^2 + c*x^4)^13,x]","\frac{1}{28} \left(a-b x^2-c x^4\right)^{14}","\frac{1}{28} \left(a-b x^2-c x^4\right)^{14}",1,"(a - b*x^2 - c*x^4)^14/28","A",2,2,26,0.07692,1,"{1247, 629}"
99,1,20,0,0.3103043,"\int x^2 \left(b+2 c x^3\right) \left(-a+b x^3+c x^6\right)^{13} \, dx","Int[x^2*(b + 2*c*x^3)*(-a + b*x^3 + c*x^6)^13,x]","\frac{1}{42} \left(a-b x^3-c x^6\right)^{14}","\frac{1}{42} \left(a-b x^3-c x^6\right)^{14}",1,"(a - b*x^3 - c*x^6)^14/42","A",2,2,28,0.07143,1,"{1468, 629}"
100,1,25,0,0.05999,"\int x^{-1+n} \left(b+2 c x^n\right) \left(-a+b x^n+c x^{2 n}\right)^{13} \, dx","Int[x^(-1 + n)*(b + 2*c*x^n)*(-a + b*x^n + c*x^(2*n))^13,x]","\frac{\left(a-b x^n-c x^{2 n}\right)^{14}}{14 n}","\frac{\left(a-b x^n-c x^{2 n}\right)^{14}}{14 n}",1,"(a - b*x^n - c*x^(2*n))^14/(14*n)","A",2,2,32,0.06250,1,"{1468, 629}"
101,1,15,0,0.0138468,"\int (b+2 c x) \left(b x+c x^2\right)^{13} \, dx","Int[(b + 2*c*x)*(b*x + c*x^2)^13,x]","\frac{1}{14} \left(b x+c x^2\right)^{14}","\frac{1}{14} \left(b x+c x^2\right)^{14}",1,"(b*x + c*x^2)^14/14","A",1,1,18,0.05556,1,"{629}"
102,1,16,0,0.0541807,"\int x \left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{13} \, dx","Int[x*(b + 2*c*x^2)*(b*x^2 + c*x^4)^13,x]","\frac{1}{28} x^{28} \left(b+c x^2\right)^{14}","\frac{1}{28} x^{28} \left(b+c x^2\right)^{14}",1,"(x^28*(b + c*x^2)^14)/28","A",3,3,23,0.1304,1,"{1584, 446, 74}"
103,1,16,0,0.0557805,"\int x^2 \left(b+2 c x^3\right) \left(b x^3+c x^6\right)^{13} \, dx","Int[x^2*(b + 2*c*x^3)*(b*x^3 + c*x^6)^13,x]","\frac{1}{42} x^{42} \left(b+c x^3\right)^{14}","\frac{1}{42} x^{42} \left(b+c x^3\right)^{14}",1,"(x^42*(b + c*x^3)^14)/42","A",3,3,25,0.1200,1,"{1584, 446, 74}"
104,1,21,0,0.0327483,"\int x^{-1+n} \left(b+2 c x^n\right) \left(b x^n+c x^{2 n}\right)^{13} \, dx","Int[x^(-1 + n)*(b + 2*c*x^n)*(b*x^n + c*x^(2*n))^13,x]","\frac{x^{14 n} \left(b+c x^n\right)^{14}}{14 n}","\frac{x^{14 n} \left(b+c x^n\right)^{14}}{14 n}",1,"(x^(14*n)*(b + c*x^n)^14)/(14*n)","A",3,3,29,0.1034,1,"{1584, 446, 74}"
105,1,11,0,0.0040946,"\int \frac{b+2 c x}{a+b x+c x^2} \, dx","Int[(b + 2*c*x)/(a + b*x + c*x^2),x]","\log \left(a+b x+c x^2\right)","\log \left(a+b x+c x^2\right)",1,"Log[a + b*x + c*x^2]","A",1,1,19,0.05263,1,"{628}"
106,1,17,0,0.0186135,"\int \frac{x \left(b+2 c x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x*(b + 2*c*x^2))/(a + b*x^2 + c*x^4),x]","\frac{1}{2} \log \left(a+b x^2+c x^4\right)","\frac{1}{2} \log \left(a+b x^2+c x^4\right)",1,"Log[a + b*x^2 + c*x^4]/2","A",2,2,24,0.08333,1,"{1247, 628}"
107,1,17,0,0.0237446,"\int \frac{x^2 \left(b+2 c x^3\right)}{a+b x^3+c x^6} \, dx","Int[(x^2*(b + 2*c*x^3))/(a + b*x^3 + c*x^6),x]","\frac{1}{3} \log \left(a+b x^3+c x^6\right)","\frac{1}{3} \log \left(a+b x^3+c x^6\right)",1,"Log[a + b*x^3 + c*x^6]/3","A",2,2,26,0.07692,1,"{1468, 628}"
108,1,19,0,0.0269621,"\int \frac{x^{-1+n} \left(b+2 c x^n\right)}{a+b x^n+c x^{2 n}} \, dx","Int[(x^(-1 + n)*(b + 2*c*x^n))/(a + b*x^n + c*x^(2*n)),x]","\frac{\log \left(a+b x^n+c x^{2 n}\right)}{n}","\frac{\log \left(a+b x^n+c x^{2 n}\right)}{n}",1,"Log[a + b*x^n + c*x^(2*n)]/n","A",2,2,30,0.06667,1,"{1468, 628}"
109,1,16,0,0.0045067,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^8} \, dx","Int[(b + 2*c*x)/(a + b*x + c*x^2)^8,x]","-\frac{1}{7 \left(a+b x+c x^2\right)^7}","-\frac{1}{7 \left(a+b x+c x^2\right)^7}",1,"-1/(7*(a + b*x + c*x^2)^7)","A",1,1,19,0.05263,1,"{629}"
110,1,18,0,0.019708,"\int \frac{x \left(b+2 c x^2\right)}{\left(a+b x^2+c x^4\right)^8} \, dx","Int[(x*(b + 2*c*x^2))/(a + b*x^2 + c*x^4)^8,x]","-\frac{1}{14 \left(a+b x^2+c x^4\right)^7}","-\frac{1}{14 \left(a+b x^2+c x^4\right)^7}",1,"-1/(14*(a + b*x^2 + c*x^4)^7)","A",2,2,24,0.08333,1,"{1247, 629}"
111,1,18,0,0.023087,"\int \frac{x^2 \left(b+2 c x^3\right)}{\left(a+b x^3+c x^6\right)^8} \, dx","Int[(x^2*(b + 2*c*x^3))/(a + b*x^3 + c*x^6)^8,x]","-\frac{1}{21 \left(a+b x^3+c x^6\right)^7}","-\frac{1}{21 \left(a+b x^3+c x^6\right)^7}",1,"-1/(21*(a + b*x^3 + c*x^6)^7)","A",2,2,26,0.07692,1,"{1468, 629}"
112,1,23,0,0.0266705,"\int \frac{x^{-1+n} \left(b+2 c x^n\right)}{\left(a+b x^n+c x^{2 n}\right)^8} \, dx","Int[(x^(-1 + n)*(b + 2*c*x^n))/(a + b*x^n + c*x^(2*n))^8,x]","-\frac{1}{7 n \left(a+b x^n+c x^{2 n}\right)^7}","-\frac{1}{7 n \left(a+b x^n+c x^{2 n}\right)^7}",1,"-1/(7*n*(a + b*x^n + c*x^(2*n))^7)","A",2,2,30,0.06667,1,"{1468, 629}"
113,1,13,0,0.0047574,"\int \frac{b+2 c x}{-a+b x+c x^2} \, dx","Int[(b + 2*c*x)/(-a + b*x + c*x^2),x]","\log \left(a-b x-c x^2\right)","\log \left(a-b x-c x^2\right)",1,"Log[a - b*x - c*x^2]","A",1,1,21,0.04762,1,"{628}"
114,1,19,0,0.0193331,"\int \frac{x \left(b+2 c x^2\right)}{-a+b x^2+c x^4} \, dx","Int[(x*(b + 2*c*x^2))/(-a + b*x^2 + c*x^4),x]","\frac{1}{2} \log \left(a-b x^2-c x^4\right)","\frac{1}{2} \log \left(a-b x^2-c x^4\right)",1,"Log[a - b*x^2 - c*x^4]/2","A",2,2,26,0.07692,1,"{1247, 628}"
115,1,19,0,0.0240185,"\int \frac{x^2 \left(b+2 c x^3\right)}{-a+b x^3+c x^6} \, dx","Int[(x^2*(b + 2*c*x^3))/(-a + b*x^3 + c*x^6),x]","\frac{1}{3} \log \left(a-b x^3-c x^6\right)","\frac{1}{3} \log \left(a-b x^3-c x^6\right)",1,"Log[a - b*x^3 - c*x^6]/3","A",2,2,28,0.07143,1,"{1468, 628}"
116,1,21,0,0.0288613,"\int \frac{x^{-1+n} \left(b+2 c x^n\right)}{-a+b x^n+c x^{2 n}} \, dx","Int[(x^(-1 + n)*(b + 2*c*x^n))/(-a + b*x^n + c*x^(2*n)),x]","\frac{\log \left(a-b x^n-c x^{2 n}\right)}{n}","\frac{\log \left(a-b x^n-c x^{2 n}\right)}{n}",1,"Log[a - b*x^n - c*x^(2*n)]/n","A",2,2,32,0.06250,1,"{1468, 628}"
117,1,18,0,0.004369,"\int \frac{b+2 c x}{\left(-a+b x+c x^2\right)^8} \, dx","Int[(b + 2*c*x)/(-a + b*x + c*x^2)^8,x]","\frac{1}{7 \left(a-b x-c x^2\right)^7}","\frac{1}{7 \left(a-b x-c x^2\right)^7}",1,"1/(7*(a - b*x - c*x^2)^7)","A",1,1,21,0.04762,1,"{629}"
118,1,20,0,0.0195398,"\int \frac{x \left(b+2 c x^2\right)}{\left(-a+b x^2+c x^4\right)^8} \, dx","Int[(x*(b + 2*c*x^2))/(-a + b*x^2 + c*x^4)^8,x]","\frac{1}{14 \left(a-b x^2-c x^4\right)^7}","\frac{1}{14 \left(a-b x^2-c x^4\right)^7}",1,"1/(14*(a - b*x^2 - c*x^4)^7)","A",2,2,26,0.07692,1,"{1247, 629}"
119,1,20,0,0.0244405,"\int \frac{x^2 \left(b+2 c x^3\right)}{\left(-a+b x^3+c x^6\right)^8} \, dx","Int[(x^2*(b + 2*c*x^3))/(-a + b*x^3 + c*x^6)^8,x]","\frac{1}{21 \left(a-b x^3-c x^6\right)^7}","\frac{1}{21 \left(a-b x^3-c x^6\right)^7}",1,"1/(21*(a - b*x^3 - c*x^6)^7)","A",2,2,28,0.07143,1,"{1468, 629}"
120,1,25,0,0.0290118,"\int \frac{x^{-1+n} \left(b+2 c x^n\right)}{\left(-a+b x^n+c x^{2 n}\right)^8} \, dx","Int[(x^(-1 + n)*(b + 2*c*x^n))/(-a + b*x^n + c*x^(2*n))^8,x]","\frac{1}{7 n \left(a-b x^n-c x^{2 n}\right)^7}","\frac{1}{7 n \left(a-b x^n-c x^{2 n}\right)^7}",1,"1/(7*n*(a - b*x^n - c*x^(2*n))^7)","A",2,2,32,0.06250,1,"{1468, 629}"
121,1,10,0,0.0042626,"\int \frac{b+2 c x}{b x+c x^2} \, dx","Int[(b + 2*c*x)/(b*x + c*x^2),x]","\log \left(b x+c x^2\right)","\log \left(b x+c x^2\right)",1,"Log[b*x + c*x^2]","A",1,1,18,0.05556,1,"{628}"
122,1,15,0,0.0239123,"\int \frac{x \left(b+2 c x^2\right)}{b x^2+c x^4} \, dx","Int[(x*(b + 2*c*x^2))/(b*x^2 + c*x^4),x]","\frac{1}{2} \log \left(b+c x^2\right)+\log (x)","\frac{1}{2} \log \left(b x^2+c x^4\right)",1,"Log[x] + Log[b + c*x^2]/2","A",4,3,23,0.1304,1,"{1584, 446, 72}"
123,1,15,0,0.0295228,"\int \frac{x^2 \left(b+2 c x^3\right)}{b x^3+c x^6} \, dx","Int[(x^2*(b + 2*c*x^3))/(b*x^3 + c*x^6),x]","\frac{1}{3} \log \left(b+c x^3\right)+\log (x)","\frac{1}{3} \log \left(b x^3+c x^6\right)",1,"Log[x] + Log[b + c*x^3]/3","A",4,3,25,0.1200,1,"{1584, 446, 72}"
124,1,15,0,0.0350369,"\int \frac{x^{-1+n} \left(b+2 c x^n\right)}{b x^n+c x^{2 n}} \, dx","Int[(x^(-1 + n)*(b + 2*c*x^n))/(b*x^n + c*x^(2*n)),x]","\frac{\log \left(b+c x^n\right)}{n}+\log (x)","\frac{\log \left(b+c x^n\right)}{n}+\log (x)",1,"Log[x] + Log[b + c*x^n]/n","A",4,3,29,0.1034,1,"{1584, 446, 72}"
125,1,15,0,0.0040906,"\int \frac{b+2 c x}{\left(b x+c x^2\right)^8} \, dx","Int[(b + 2*c*x)/(b*x + c*x^2)^8,x]","-\frac{1}{7 \left(b x+c x^2\right)^7}","-\frac{1}{7 \left(b x+c x^2\right)^7}",1,"-1/(7*(b*x + c*x^2)^7)","A",1,1,18,0.05556,1,"{629}"
126,1,16,0,0.0208838,"\int \frac{x \left(b+2 c x^2\right)}{\left(b x^2+c x^4\right)^8} \, dx","Int[(x*(b + 2*c*x^2))/(b*x^2 + c*x^4)^8,x]","-\frac{1}{14 x^{14} \left(b+c x^2\right)^7}","-\frac{1}{14 x^{14} \left(b+c x^2\right)^7}",1,"-1/(14*x^14*(b + c*x^2)^7)","A",3,3,23,0.1304,1,"{1584, 446, 74}"
127,1,16,0,0.0253234,"\int \frac{x^2 \left(b+2 c x^3\right)}{\left(b x^3+c x^6\right)^8} \, dx","Int[(x^2*(b + 2*c*x^3))/(b*x^3 + c*x^6)^8,x]","-\frac{1}{21 x^{21} \left(b+c x^3\right)^7}","-\frac{1}{21 x^{21} \left(b+c x^3\right)^7}",1,"-1/(21*x^21*(b + c*x^3)^7)","A",3,3,25,0.1200,1,"{1584, 446, 74}"
128,1,21,0,0.0324075,"\int \frac{x^{-1+n} \left(b+2 c x^n\right)}{\left(b x^n+c x^{2 n}\right)^8} \, dx","Int[(x^(-1 + n)*(b + 2*c*x^n))/(b*x^n + c*x^(2*n))^8,x]","-\frac{x^{-7 n}}{7 n \left(b+c x^n\right)^7}","-\frac{x^{-7 n}}{7 n \left(b+c x^n\right)^7}",1,"-1/(7*n*x^(7*n)*(b + c*x^n)^7)","A",3,3,29,0.1034,1,"{1584, 446, 74}"
129,1,20,0,0.0054882,"\int (b+2 c x) \left(a+b x+c x^2\right)^p \, dx","Int[(b + 2*c*x)*(a + b*x + c*x^2)^p,x]","\frac{\left(a+b x+c x^2\right)^{p+1}}{p+1}","\frac{\left(a+b x+c x^2\right)^{p+1}}{p+1}",1,"(a + b*x + c*x^2)^(1 + p)/(1 + p)","A",1,1,19,0.05263,1,"{629}"
130,1,25,0,0.0191148,"\int x \left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^p \, dx","Int[x*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^p,x]","\frac{\left(a+b x^2+c x^4\right)^{p+1}}{2 (p+1)}","\frac{\left(a+b x^2+c x^4\right)^{p+1}}{2 (p+1)}",1,"(a + b*x^2 + c*x^4)^(1 + p)/(2*(1 + p))","A",2,2,24,0.08333,1,"{1247, 629}"
131,1,25,0,0.0236525,"\int x^2 \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^p \, dx","Int[x^2*(b + 2*c*x^3)*(a + b*x^3 + c*x^6)^p,x]","\frac{\left(a+b x^3+c x^6\right)^{p+1}}{3 (p+1)}","\frac{\left(a+b x^3+c x^6\right)^{p+1}}{3 (p+1)}",1,"(a + b*x^3 + c*x^6)^(1 + p)/(3*(1 + p))","A",2,2,26,0.07692,1,"{1468, 629}"
132,1,27,0,0.0284039,"\int x^{-1+n} \left(b+2 c x^n\right) \left(a+b x^n+c x^{2 n}\right)^p \, dx","Int[x^(-1 + n)*(b + 2*c*x^n)*(a + b*x^n + c*x^(2*n))^p,x]","\frac{\left(a+b x^n+c x^{2 n}\right)^{p+1}}{n (p+1)}","\frac{\left(a+b x^n+c x^{2 n}\right)^{p+1}}{n (p+1)}",1,"(a + b*x^n + c*x^(2*n))^(1 + p)/(n*(1 + p))","A",2,2,30,0.06667,1,"{1468, 629}"
133,1,22,0,0.0050084,"\int (b+2 c x) \left(-a+b x+c x^2\right)^p \, dx","Int[(b + 2*c*x)*(-a + b*x + c*x^2)^p,x]","\frac{\left(-a+b x+c x^2\right)^{p+1}}{p+1}","\frac{\left(-a+b x+c x^2\right)^{p+1}}{p+1}",1,"(-a + b*x + c*x^2)^(1 + p)/(1 + p)","A",1,1,21,0.04762,1,"{629}"
134,1,27,0,0.0195965,"\int x \left(b+2 c x^2\right) \left(-a+b x^2+c x^4\right)^p \, dx","Int[x*(b + 2*c*x^2)*(-a + b*x^2 + c*x^4)^p,x]","\frac{\left(-a+b x^2+c x^4\right)^{p+1}}{2 (p+1)}","\frac{\left(-a+b x^2+c x^4\right)^{p+1}}{2 (p+1)}",1,"(-a + b*x^2 + c*x^4)^(1 + p)/(2*(1 + p))","A",2,2,26,0.07692,1,"{1247, 629}"
135,1,27,0,0.0247507,"\int x^2 \left(b+2 c x^3\right) \left(-a+b x^3+c x^6\right)^p \, dx","Int[x^2*(b + 2*c*x^3)*(-a + b*x^3 + c*x^6)^p,x]","\frac{\left(-a+b x^3+c x^6\right)^{p+1}}{3 (p+1)}","\frac{\left(-a+b x^3+c x^6\right)^{p+1}}{3 (p+1)}",1,"(-a + b*x^3 + c*x^6)^(1 + p)/(3*(1 + p))","A",2,2,28,0.07143,1,"{1468, 629}"
136,1,29,0,0.0282607,"\int x^{-1+n} \left(b+2 c x^n\right) \left(-a+b x^n+c x^{2 n}\right)^p \, dx","Int[x^(-1 + n)*(b + 2*c*x^n)*(-a + b*x^n + c*x^(2*n))^p,x]","\frac{\left(-a+b x^n+c x^{2 n}\right)^{p+1}}{n (p+1)}","\frac{\left(-a+b x^n+c x^{2 n}\right)^{p+1}}{n (p+1)}",1,"(-a + b*x^n + c*x^(2*n))^(1 + p)/(n*(1 + p))","A",2,2,32,0.06250,1,"{1468, 629}"
137,1,19,0,0.004136,"\int (b+2 c x) \left(b x+c x^2\right)^p \, dx","Int[(b + 2*c*x)*(b*x + c*x^2)^p,x]","\frac{\left(b x+c x^2\right)^{p+1}}{p+1}","\frac{\left(b x+c x^2\right)^{p+1}}{p+1}",1,"(b*x + c*x^2)^(1 + p)/(1 + p)","A",1,1,18,0.05556,1,"{629}"
138,1,24,0,0.0141711,"\int x \left(b+2 c x^2\right) \left(b x^2+c x^4\right)^p \, dx","Int[x*(b + 2*c*x^2)*(b*x^2 + c*x^4)^p,x]","\frac{\left(b x^2+c x^4\right)^{p+1}}{2 (p+1)}","\frac{\left(b x^2+c x^4\right)^{p+1}}{2 (p+1)}",1,"(b*x^2 + c*x^4)^(1 + p)/(2*(1 + p))","A",1,1,23,0.04348,1,"{1588}"
139,1,24,0,0.0196933,"\int x^2 \left(b+2 c x^3\right) \left(b x^3+c x^6\right)^p \, dx","Int[x^2*(b + 2*c*x^3)*(b*x^3 + c*x^6)^p,x]","\frac{\left(b x^3+c x^6\right)^{p+1}}{3 (p+1)}","\frac{\left(b x^3+c x^6\right)^{p+1}}{3 (p+1)}",1,"(b*x^3 + c*x^6)^(1 + p)/(3*(1 + p))","A",1,1,25,0.04000,1,"{1588}"
140,1,26,0,0.0789861,"\int x^{-1+n} \left(b+2 c x^n\right) \left(b x^n+c x^{2 n}\right)^p \, dx","Int[x^(-1 + n)*(b + 2*c*x^n)*(b*x^n + c*x^(2*n))^p,x]","\frac{\left(b x^n+c x^{2 n}\right)^{p+1}}{n (p+1)}","\frac{\left(b x^n+c x^{2 n}\right)^{p+1}}{n (p+1)}",1,"(b*x^n + c*x^(2*n))^(1 + p)/(n*(1 + p))","A",2,2,29,0.06897,1,"{2034, 629}"
141,1,196,0,0.2889647,"\int \frac{(f x)^m \left(d+e x^n\right)}{a+b x^n+c x^{2 n}} \, dx","Int[((f*x)^m*(d + e*x^n))/(a + b*x^n + c*x^(2*n)),x]","\frac{(f x)^{m+1} \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{f (m+1) \left(b-\sqrt{b^2-4 a c}\right)}+\frac{(f x)^{m+1} \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \left(\sqrt{b^2-4 a c}+b\right)}","\frac{(f x)^{m+1} \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{f (m+1) \left(b-\sqrt{b^2-4 a c}\right)}+\frac{(f x)^{m+1} \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \left(\sqrt{b^2-4 a c}+b\right)}",1,"((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*f*(1 + m)) + ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*f*(1 + m))","A",4,2,29,0.06897,1,"{1560, 364}"
142,1,374,0,1.3802854,"\int \frac{(f x)^m \left(d+e x^n\right)}{\left(a+b x^n+c x^{2 n}\right)^2} \, dx","Int[((f*x)^m*(d + e*x^n))/(a + b*x^n + c*x^(2*n))^2,x]","-\frac{c (f x)^{m+1} \left((m-n+1) (b d-2 a e)-\frac{2 a b e n+4 a c d (m-2 n+1)+b^2 (-d) (m-n+1)}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{a f (m+1) n \left(b^2-4 a c\right) \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (f x)^{m+1} \left(\frac{2 a b e n+4 a c d (m-2 n+1)+b^2 (-d) (m-n+1)}{\sqrt{b^2-4 a c}}+(m-n+1) (b d-2 a e)\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a f (m+1) n \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f x)^{m+1} \left(c x^n (b d-2 a e)-a b e-2 a c d+b^2 d\right)}{a f n \left(b^2-4 a c\right) \left(a+b x^n+c x^{2 n}\right)}","-\frac{c (f x)^{m+1} \left((m-n+1) (b d-2 a e)-\frac{2 a b e n+4 a c d (m-2 n+1)+b^2 (-d) (m-n+1)}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{a f (m+1) n \left(b^2-4 a c\right) \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (f x)^{m+1} \left(\frac{2 a b e n+4 a c d (m-2 n+1)+b^2 (-d) (m-n+1)}{\sqrt{b^2-4 a c}}+(m-n+1) (b d-2 a e)\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a f (m+1) n \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f x)^{m+1} \left(c x^n (b d-2 a e)-a b e-2 a c d+b^2 d\right)}{a f n \left(b^2-4 a c\right) \left(a+b x^n+c x^{2 n}\right)}",1,"((f*x)^(1 + m)*(b^2*d - 2*a*c*d - a*b*e + c*(b*d - 2*a*e)*x^n))/(a*(b^2 - 4*a*c)*f*n*(a + b*x^n + c*x^(2*n))) - (c*((b*d - 2*a*e)*(1 + m - n) - (4*a*c*d*(1 + m - 2*n) - b^2*d*(1 + m - n) + 2*a*b*e*n)/Sqrt[b^2 - 4*a*c])*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/(a*(b^2 - 4*a*c)*(b - Sqrt[b^2 - 4*a*c])*f*(1 + m)*n) - (c*((b*d - 2*a*e)*(1 + m - n) + (4*a*c*d*(1 + m - 2*n) - b^2*d*(1 + m - n) + 2*a*b*e*n)/Sqrt[b^2 - 4*a*c])*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(a*(b^2 - 4*a*c)*(b + Sqrt[b^2 - 4*a*c])*f*(1 + m)*n)","A",5,3,29,0.1034,1,"{1558, 1560, 364}"
143,1,816,0,4.5520468,"\int \frac{(f x)^m \left(d+e x^n\right)}{\left(a+b x^n+c x^{2 n}\right)^3} \, dx","Int[((f*x)^m*(d + e*x^n))/(a + b*x^n + c*x^(2*n))^3,x]","-\frac{c \left(\left(-d (m-2 n+1) b^3+a e (m+1) b^2+2 a c d (2 m-7 n+2) b-4 a^2 c e (m-3 n+1)\right) (m-n+1)+\frac{-d \left(m^2+(2-3 n) m+2 n^2-3 n+1\right) b^4+a e (m+1) (m-n+1) b^3+6 a c d \left(m^2+(2-4 n) m+3 n^2-4 n+1\right) b^2-4 a^2 c e \left(m^2+(2-n) m-3 n^2-n+1\right) b-8 a^2 c^2 d \left(m^2+(2-6 n) m+8 n^2-6 n+1\right)}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right) (f x)^{m+1}}{2 a^2 \left(b^2-4 a c\right)^2 \left(b-\sqrt{b^2-4 a c}\right) f (m+1) n^2}-\frac{c \left(\left(-d (m-2 n+1) b^3+a e (m+1) b^2+2 a c d (2 m-7 n+2) b-4 a^2 c e (m-3 n+1)\right) (m-n+1)-\frac{-d \left(m^2+(2-3 n) m+2 n^2-3 n+1\right) b^4+a e (m+1) (m-n+1) b^3+6 a c d \left(m^2+(2-4 n) m+3 n^2-4 n+1\right) b^2-4 a^2 c e \left(m^2+(2-n) m-3 n^2-n+1\right) b-8 a^2 c^2 d \left(m^2+(2-6 n) m+8 n^2-6 n+1\right)}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right) (f x)^{m+1}}{2 a^2 \left(b^2-4 a c\right)^2 \left(b+\sqrt{b^2-4 a c}\right) f (m+1) n^2}+\frac{\left(c \left(-d (m-2 n+1) b^3+a e (m+1) b^2+2 a c d (2 m-7 n+2) b-4 a^2 c e (m-3 n+1)\right) x^n+\left(b^2-2 a c\right) \left(-d (m-2 n+1) b^2+a e (m+1) b+2 a c d (m-4 n+1)\right)+a b c (b d-2 a e) (m-3 n+1)\right) (f x)^{m+1}}{2 a^2 \left(b^2-4 a c\right)^2 f n^2 \left(b x^n+c x^{2 n}+a\right)}+\frac{\left(c (b d-2 a e) x^n+b^2 d-2 a c d-a b e\right) (f x)^{m+1}}{2 a \left(b^2-4 a c\right) f n \left(b x^n+c x^{2 n}+a\right)^2}","-\frac{c \left(\left(-d (m-2 n+1) b^3+a e (m+1) b^2+2 a c d (2 m-7 n+2) b-4 a^2 c e (m-3 n+1)\right) (m-n+1)+\frac{-d \left(m^2+(2-3 n) m+2 n^2-3 n+1\right) b^4+a e (m+1) (m-n+1) b^3+6 a c d \left(m^2+(2-4 n) m+3 n^2-4 n+1\right) b^2-4 a^2 c e \left(m^2+(2-n) m-3 n^2-n+1\right) b-8 a^2 c^2 d \left(m^2+(2-6 n) m+8 n^2-6 n+1\right)}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right) (f x)^{m+1}}{2 a^2 \left(b^2-4 a c\right)^2 \left(b-\sqrt{b^2-4 a c}\right) f (m+1) n^2}-\frac{c \left(\left(-d (m-2 n+1) b^3+a e (m+1) b^2+2 a c d (2 m-7 n+2) b-4 a^2 c e (m-3 n+1)\right) (m-n+1)-\frac{-d \left(m^2+(2-3 n) m+2 n^2-3 n+1\right) b^4+a e (m+1) (m-n+1) b^3+6 a c d \left(m^2+(2-4 n) m+3 n^2-4 n+1\right) b^2-4 a^2 c e \left(m^2+(2-n) m-3 n^2-n+1\right) b-8 a^2 c^2 d \left(m^2+(2-6 n) m+8 n^2-6 n+1\right)}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right) (f x)^{m+1}}{2 a^2 \left(b^2-4 a c\right)^2 \left(b+\sqrt{b^2-4 a c}\right) f (m+1) n^2}+\frac{\left(c \left(-d (m-2 n+1) b^3+a e (m+1) b^2+2 a c d (2 m-7 n+2) b-4 a^2 c e (m-3 n+1)\right) x^n+\left(b^2-2 a c\right) \left(-d (m-2 n+1) b^2+a e (m+1) b+2 a c d (m-4 n+1)\right)+a b c (b d-2 a e) (m-3 n+1)\right) (f x)^{m+1}}{2 a^2 \left(b^2-4 a c\right)^2 f n^2 \left(b x^n+c x^{2 n}+a\right)}+\frac{\left(c (b d-2 a e) x^n+b^2 d-2 a c d-a b e\right) (f x)^{m+1}}{2 a \left(b^2-4 a c\right) f n \left(b x^n+c x^{2 n}+a\right)^2}",1,"((f*x)^(1 + m)*(b^2*d - 2*a*c*d - a*b*e + c*(b*d - 2*a*e)*x^n))/(2*a*(b^2 - 4*a*c)*f*n*(a + b*x^n + c*x^(2*n))^2) + ((f*x)^(1 + m)*((b^2 - 2*a*c)*(a*b*e*(1 + m) + 2*a*c*d*(1 + m - 4*n) - b^2*d*(1 + m - 2*n)) + a*b*c*(b*d - 2*a*e)*(1 + m - 3*n) + c*(a*b^2*e*(1 + m) + 2*a*b*c*d*(2 + 2*m - 7*n) - 4*a^2*c*e*(1 + m - 3*n) - b^3*d*(1 + m - 2*n))*x^n))/(2*a^2*(b^2 - 4*a*c)^2*f*n^2*(a + b*x^n + c*x^(2*n))) - (c*((a*b^2*e*(1 + m) + 2*a*b*c*d*(2 + 2*m - 7*n) - 4*a^2*c*e*(1 + m - 3*n) - b^3*d*(1 + m - 2*n))*(1 + m - n) + (a*b^3*e*(1 + m)*(1 + m - n) - 4*a^2*b*c*e*(1 + m^2 + m*(2 - n) - n - 3*n^2) - b^4*d*(1 + m^2 + m*(2 - 3*n) - 3*n + 2*n^2) + 6*a*b^2*c*d*(1 + m^2 + m*(2 - 4*n) - 4*n + 3*n^2) - 8*a^2*c^2*d*(1 + m^2 + m*(2 - 6*n) - 6*n + 8*n^2))/Sqrt[b^2 - 4*a*c])*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/(2*a^2*(b^2 - 4*a*c)^2*(b - Sqrt[b^2 - 4*a*c])*f*(1 + m)*n^2) - (c*((a*b^2*e*(1 + m) + 2*a*b*c*d*(2 + 2*m - 7*n) - 4*a^2*c*e*(1 + m - 3*n) - b^3*d*(1 + m - 2*n))*(1 + m - n) - (a*b^3*e*(1 + m)*(1 + m - n) - 4*a^2*b*c*e*(1 + m^2 + m*(2 - n) - n - 3*n^2) - b^4*d*(1 + m^2 + m*(2 - 3*n) - 3*n + 2*n^2) + 6*a*b^2*c*d*(1 + m^2 + m*(2 - 4*n) - 4*n + 3*n^2) - 8*a^2*c^2*d*(1 + m^2 + m*(2 - 6*n) - 6*n + 8*n^2))/Sqrt[b^2 - 4*a*c])*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*a^2*(b^2 - 4*a*c)^2*(b + Sqrt[b^2 - 4*a*c])*f*(1 + m)*n^2)","A",6,3,29,0.1034,1,"{1558, 1560, 364}"
144,1,47,0,0.062168,"\int \frac{\sqrt[3]{c}-2 \sqrt[3]{d} \sqrt[3]{x}}{c \sqrt[3]{d} x^{2/3}-c^{2/3} d^{2/3} x+\sqrt[3]{c} d x^{4/3}} \, dx","Int[(c^(1/3) - 2*d^(1/3)*x^(1/3))/(c*d^(1/3)*x^(2/3) - c^(2/3)*d^(2/3)*x + c^(1/3)*d*x^(4/3)),x]","-\frac{3 \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{x}+d^{2/3} x^{2/3}\right)}{\sqrt[3]{c} d^{2/3}}","-\frac{3 \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{x}+d^{2/3} x^{2/3}\right)}{\sqrt[3]{c} d^{2/3}}",1,"(-3*Log[c^(2/3) - c^(1/3)*d^(1/3)*x^(1/3) + d^(2/3)*x^(2/3)])/(c^(1/3)*d^(2/3))","A",3,3,59,0.05085,1,"{1594, 1468, 628}"
145,1,245,0,0.5399412,"\int \frac{(f x)^m \left(d+e x^n\right)^q}{a+b x^n+c x^{2 n}} \, dx","Int[((f*x)^m*(d + e*x^n)^q)/(a + b*x^n + c*x^(2*n)),x]","\frac{2 c (f x)^{m+1} \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{m+1}{n};1,-q;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{f (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (f x)^{m+1} \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{m+1}{n};1,-q;\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{f (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}","\frac{2 c (f x)^{m+1} \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{m+1}{n};1,-q;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{f (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (f x)^{m+1} \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{m+1}{n};1,-q;\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{f (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}",1,"(2*c*(f*x)^(1 + m)*(d + e*x^n)^q*AppellF1[(1 + m)/n, 1, -q, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*f*(1 + m)*(1 + (e*x^n)/d)^q) - (2*c*(f*x)^(1 + m)*(d + e*x^n)^q*AppellF1[(1 + m)/n, 1, -q, (1 + m + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*f*(1 + m)*(1 + (e*x^n)/d)^q)","A",5,3,31,0.09677,1,"{1556, 511, 510}"
146,1,210,0,0.5012035,"\int \frac{x^2 \left(d+e x^n\right)^q}{a+b x^n+c x^{2 n}} \, dx","Int[(x^2*(d + e*x^n)^q)/(a + b*x^n + c*x^(2*n)),x]","-\frac{2 c x^3 \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{3}{n};1,-q;\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{3 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}-\frac{2 c x^3 \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{3}{n};1,-q;\frac{n+3}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{3 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}","-\frac{2 c x^3 \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{3}{n};1,-q;\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{3 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}-\frac{2 c x^3 \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{3}{n};1,-q;\frac{n+3}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{3 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}",1,"(-2*c*x^3*(d + e*x^n)^q*AppellF1[3/n, 1, -q, (3 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/(3*(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])*(1 + (e*x^n)/d)^q) - (2*c*x^3*(d + e*x^n)^q*AppellF1[3/n, 1, -q, (3 + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/(3*(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*(1 + (e*x^n)/d)^q)","A",5,3,29,0.1034,1,"{1556, 511, 510}"
147,1,206,0,0.3757388,"\int \frac{x \left(d+e x^n\right)^q}{a+b x^n+c x^{2 n}} \, dx","Int[(x*(d + e*x^n)^q)/(a + b*x^n + c*x^(2*n)),x]","-\frac{c x^2 \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{2}{n};1,-q;\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{c x^2 \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{2}{n};1,-q;\frac{n+2}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}","-\frac{c x^2 \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{2}{n};1,-q;\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{c x^2 \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{2}{n};1,-q;\frac{n+2}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}",1,"-((c*x^2*(d + e*x^n)^q*AppellF1[2/n, 1, -q, (2 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/((b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])*(1 + (e*x^n)/d)^q)) - (c*x^2*(d + e*x^n)^q*AppellF1[2/n, 1, -q, (2 + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/((b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*(1 + (e*x^n)/d)^q)","A",5,3,27,0.1111,1,"{1556, 511, 510}"
148,1,194,0,0.2996774,"\int \frac{\left(d+e x^n\right)^q}{a+b x^n+c x^{2 n}} \, dx","Int[(d + e*x^n)^q/(a + b*x^n + c*x^(2*n)),x]","-\frac{2 c x \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{1}{n};1,-q;1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{2 c x \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{1}{n};1,-q;1+\frac{1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}","-\frac{2 c x \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{1}{n};1,-q;1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{2 c x \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(\frac{1}{n};1,-q;1+\frac{1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}",1,"(-2*c*x*(d + e*x^n)^q*AppellF1[n^(-1), 1, -q, 1 + n^(-1), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/((b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])*(1 + (e*x^n)/d)^q) - (2*c*x*(d + e*x^n)^q*AppellF1[n^(-1), 1, -q, 1 + n^(-1), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/((b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*(1 + (e*x^n)/d)^q)","A",5,3,26,0.1154,1,"{1428, 430, 429}"
149,1,263,0,0.733565,"\int \frac{\left(d+e x^n\right)^q}{x \left(a+b x^n+c x^{2 n}\right)} \, dx","Int[(d + e*x^n)^q/(x*(a + b*x^n + c*x^(2*n))),x]","\frac{c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \left(d+e x^n\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^n+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{a n (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \left(d+e x^n\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^n+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{a n (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{\left(d+e x^n\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{e x^n}{d}+1\right)}{a d n (q+1)}","\frac{c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \left(d+e x^n\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^n+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{a n (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \left(d+e x^n\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^n+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{a n (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{\left(d+e x^n\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{e x^n}{d}+1\right)}{a d n (q+1)}",1,"(c*(1 + b/Sqrt[b^2 - 4*a*c])*(d + e*x^n)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^n))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(a*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*n*(1 + q)) + (c*(1 - b/Sqrt[b^2 - 4*a*c])*(d + e*x^n)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^n))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(a*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*n*(1 + q)) - ((d + e*x^n)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, 1 + (e*x^n)/d])/(a*d*n*(1 + q))","A",8,5,29,0.1724,1,"{1474, 960, 65, 830, 68}"
150,1,212,0,0.488911,"\int \frac{\left(d+e x^n\right)^q}{x^2 \left(a+b x^n+c x^{2 n}\right)} \, dx","Int[(d + e*x^n)^q/(x^2*(a + b*x^n + c*x^(2*n))),x]","\frac{2 c \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(-\frac{1}{n};1,-q;-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{x \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{2 c \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(-\frac{1}{n};1,-q;-\frac{1-n}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{x \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}","\frac{2 c \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(-\frac{1}{n};1,-q;-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{x \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{2 c \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(-\frac{1}{n};1,-q;-\frac{1-n}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{x \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}",1,"(2*c*(d + e*x^n)^q*AppellF1[-n^(-1), 1, -q, -((1 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/((b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])*x*(1 + (e*x^n)/d)^q) + (2*c*(d + e*x^n)^q*AppellF1[-n^(-1), 1, -q, -((1 - n)/n), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/((b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*x*(1 + (e*x^n)/d)^q)","A",5,3,29,0.1034,1,"{1556, 511, 510}"
151,1,210,0,0.4756194,"\int \frac{\left(d+e x^n\right)^q}{x^3 \left(a+b x^n+c x^{2 n}\right)} \, dx","Int[(d + e*x^n)^q/(x^3*(a + b*x^n + c*x^(2*n))),x]","\frac{c \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(-\frac{2}{n};1,-q;-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{x^2 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{c \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(-\frac{2}{n};1,-q;-\frac{2-n}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{x^2 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}","\frac{c \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(-\frac{2}{n};1,-q;-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{x^2 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{c \left(d+e x^n\right)^q \left(\frac{e x^n}{d}+1\right)^{-q} F_1\left(-\frac{2}{n};1,-q;-\frac{2-n}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}},-\frac{e x^n}{d}\right)}{x^2 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}",1,"(c*(d + e*x^n)^q*AppellF1[-2/n, 1, -q, -((2 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/((b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])*x^2*(1 + (e*x^n)/d)^q) + (c*(d + e*x^n)^q*AppellF1[-2/n, 1, -q, -((2 - n)/n), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^n)/d)])/((b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*x^2*(1 + (e*x^n)/d)^q)","A",5,3,29,0.1034,1,"{1556, 511, 510}"
152,1,498,0,0.6094878,"\int (f x)^m \left(d+e x^n\right)^2 \left(a+b x^n+c x^{2 n}\right)^p \, dx","Int[(f*x)^m*(d + e*x^n)^2*(a + b*x^n + c*x^(2*n))^p,x]","\frac{d^2 (f x)^{m+1} \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+1}{n};-p,-p;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1)}+\frac{2 d e x^{n+1} (f x)^m \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+n+1}{n};-p,-p;\frac{m+2 n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{m+n+1}+\frac{e^2 x^{2 n+1} (f x)^m \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+2 n+1}{n};-p,-p;\frac{m+3 n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{m+2 n+1}","\frac{d^2 (f x)^{m+1} \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+1}{n};-p,-p;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1)}+\frac{2 d e x^{n+1} (f x)^m \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+n+1}{n};-p,-p;\frac{m+2 n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{m+n+1}+\frac{e^2 x^{2 n+1} (f x)^m \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+2 n+1}{n};-p,-p;\frac{m+3 n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{m+2 n+1}",1,"(d^2*(f*x)^(1 + m)*(a + b*x^n + c*x^(2*n))^p*AppellF1[(1 + m)/n, -p, -p, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(f*(1 + m)*(1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]))^p) + (2*d*e*x^(1 + n)*(f*x)^m*(a + b*x^n + c*x^(2*n))^p*AppellF1[(1 + m + n)/n, -p, -p, (1 + m + 2*n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/((1 + m + n)*(1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]))^p) + (e^2*x^(1 + 2*n)*(f*x)^m*(a + b*x^n + c*x^(2*n))^p*AppellF1[(1 + m + 2*n)/n, -p, -p, (1 + m + 3*n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/((1 + m + 2*n)*(1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",10,4,31,0.1290,1,"{1560, 1385, 510, 20}"
153,1,323,0,0.37063,"\int (f x)^m \left(d+e x^n\right) \left(a+b x^n+c x^{2 n}\right)^p \, dx","Int[(f*x)^m*(d + e*x^n)*(a + b*x^n + c*x^(2*n))^p,x]","\frac{d (f x)^{m+1} \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+1}{n};-p,-p;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1)}+\frac{e x^{n+1} (f x)^m \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+n+1}{n};-p,-p;\frac{m+2 n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{m+n+1}","\frac{d (f x)^{m+1} \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+1}{n};-p,-p;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1)}+\frac{e x^{n+1} (f x)^m \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+n+1}{n};-p,-p;\frac{m+2 n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{m+n+1}",1,"(d*(f*x)^(1 + m)*(a + b*x^n + c*x^(2*n))^p*AppellF1[(1 + m)/n, -p, -p, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(f*(1 + m)*(1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]))^p) + (e*x^(1 + n)*(f*x)^m*(a + b*x^n + c*x^(2*n))^p*AppellF1[(1 + m + n)/n, -p, -p, (1 + m + 2*n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/((1 + m + n)*(1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",7,4,29,0.1379,1,"{1560, 1385, 510, 20}"
154,1,158,0,0.1238369,"\int (f x)^m \left(a+b x^n+c x^{2 n}\right)^p \, dx","Int[(f*x)^m*(a + b*x^n + c*x^(2*n))^p,x]","\frac{(f x)^{m+1} \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+1}{n};-p,-p;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1)}","\frac{(f x)^{m+1} \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+1}{n};-p,-p;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1)}",1,"((f*x)^(1 + m)*(a + b*x^n + c*x^(2*n))^p*AppellF1[(1 + m)/n, -p, -p, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(f*(1 + m)*(1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,22,0.09091,1,"{1385, 510}"
155,0,0,0,0.0255954,"\int \frac{(f x)^m \left(a+b x^n+c x^{2 n}\right)^p}{d+e x^n} \, dx","Int[((f*x)^m*(a + b*x^n + c*x^(2*n))^p)/(d + e*x^n),x]","\int \frac{(f x)^m \left(a+b x^n+c x^{2 n}\right)^p}{d+e x^n} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b x^n+c x^{2 n}\right)^p}{d+e x^n},x\right)",0,"Defer[Int][((f*x)^m*(a + b*x^n + c*x^(2*n))^p)/(d + e*x^n), x]","A",0,0,0,0,-1,"{}"
156,0,0,0,0.0251436,"\int \frac{(f x)^m \left(a+b x^n+c x^{2 n}\right)^p}{\left(d+e x^n\right)^2} \, dx","Int[((f*x)^m*(a + b*x^n + c*x^(2*n))^p)/(d + e*x^n)^2,x]","\int \frac{(f x)^m \left(a+b x^n+c x^{2 n}\right)^p}{\left(d+e x^n\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b x^n+c x^{2 n}\right)^p}{\left(d+e x^n\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*x^n + c*x^(2*n))^p)/(d + e*x^n)^2, x]","A",0,0,0,0,-1,"{}"