1,1,210,0,0.2698045,"\int (e x)^m \left(a+b x^n\right)^3 \left(A+B x^n\right) \left(c+d x^n\right) \, dx","Int[(e*x)^m*(a + b*x^n)^3*(A + B*x^n)*(c + d*x^n),x]","\frac{a^2 x^{n+1} (e x)^m (a A d+a B c+3 A b c)}{m+n+1}+\frac{a^3 A c (e x)^{m+1}}{e (m+1)}+\frac{b^2 x^{4 n+1} (e x)^m (3 a B d+A b d+b B c)}{m+4 n+1}+\frac{a x^{2 n+1} (e x)^m (3 A b (a d+b c)+a B (a d+3 b c))}{m+2 n+1}+\frac{b x^{3 n+1} (e x)^m (A b (3 a d+b c)+3 a B (a d+b c))}{m+3 n+1}+\frac{b^3 B d x^{5 n+1} (e x)^m}{m+5 n+1}","\frac{a^2 x^{n+1} (e x)^m (a A d+a B c+3 A b c)}{m+n+1}+\frac{a^3 A c (e x)^{m+1}}{e (m+1)}+\frac{b^2 x^{4 n+1} (e x)^m (3 a B d+A b d+b B c)}{m+4 n+1}+\frac{a x^{2 n+1} (e x)^m (3 A b (a d+b c)+a B (a d+3 b c))}{m+2 n+1}+\frac{b x^{3 n+1} (e x)^m (A b (3 a d+b c)+3 a B (a d+b c))}{m+3 n+1}+\frac{b^3 B d x^{5 n+1} (e x)^m}{m+5 n+1}",1,"(a^2*(3*A*b*c + a*B*c + a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (a*(3*A*b*(b*c + a*d) + a*B*(3*b*c + a*d))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + (b*(3*a*B*(b*c + a*d) + A*b*(b*c + 3*a*d))*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (b^2*(b*B*c + A*b*d + 3*a*B*d)*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (b^3*B*d*x^(1 + 5*n)*(e*x)^m)/(1 + m + 5*n) + (a^3*A*c*(e*x)^(1 + m))/(e*(1 + m))","A",12,3,29,0.1034,1,"{570, 20, 30}"
2,1,160,0,0.1764074,"\int (e x)^m \left(a+b x^n\right)^2 \left(A+B x^n\right) \left(c+d x^n\right) \, dx","Int[(e*x)^m*(a + b*x^n)^2*(A + B*x^n)*(c + d*x^n),x]","\frac{a^2 A c (e x)^{m+1}}{e (m+1)}+\frac{a x^{n+1} (e x)^m (a A d+a B c+2 A b c)}{m+n+1}+\frac{x^{2 n+1} (e x)^m (A b (2 a d+b c)+a B (a d+2 b c))}{m+2 n+1}+\frac{b x^{3 n+1} (e x)^m (2 a B d+A b d+b B c)}{m+3 n+1}+\frac{b^2 B d x^{4 n+1} (e x)^m}{m+4 n+1}","\frac{a^2 A c (e x)^{m+1}}{e (m+1)}+\frac{a x^{n+1} (e x)^m (a A d+a B c+2 A b c)}{m+n+1}+\frac{x^{2 n+1} (e x)^m (A b (2 a d+b c)+a B (a d+2 b c))}{m+2 n+1}+\frac{b x^{3 n+1} (e x)^m (2 a B d+A b d+b B c)}{m+3 n+1}+\frac{b^2 B d x^{4 n+1} (e x)^m}{m+4 n+1}",1,"(a*(2*A*b*c + a*B*c + a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + ((a*B*(2*b*c + a*d) + A*b*(b*c + 2*a*d))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + (b*(b*B*c + A*b*d + 2*a*B*d)*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (b^2*B*d*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (a^2*A*c*(e*x)^(1 + m))/(e*(1 + m))","A",10,3,29,0.1034,1,"{570, 20, 30}"
3,1,108,0,0.0838475,"\int (e x)^m \left(a+b x^n\right) \left(A+B x^n\right) \left(c+d x^n\right) \, dx","Int[(e*x)^m*(a + b*x^n)*(A + B*x^n)*(c + d*x^n),x]","\frac{x^{n+1} (e x)^m (a A d+a B c+A b c)}{m+n+1}+\frac{x^{2 n+1} (e x)^m (a B d+A b d+b B c)}{m+2 n+1}+\frac{a A c (e x)^{m+1}}{e (m+1)}+\frac{b B d x^{3 n+1} (e x)^m}{m+3 n+1}","\frac{x^{n+1} (e x)^m (a A d+a B c+A b c)}{m+n+1}+\frac{x^{2 n+1} (e x)^m (a B d+A b d+b B c)}{m+2 n+1}+\frac{a A c (e x)^{m+1}}{e (m+1)}+\frac{b B d x^{3 n+1} (e x)^m}{m+3 n+1}",1,"((A*b*c + a*B*c + a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + ((b*B*c + A*b*d + a*B*d)*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + (b*B*d*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (a*A*c*(e*x)^(1 + m))/(e*(1 + m))","A",8,3,27,0.1111,1,"{570, 20, 30}"
4,1,66,0,0.0399767,"\int (e x)^m \left(A+B x^n\right) \left(c+d x^n\right) \, dx","Int[(e*x)^m*(A + B*x^n)*(c + d*x^n),x]","\frac{x^{n+1} (e x)^m (A d+B c)}{m+n+1}+\frac{A c (e x)^{m+1}}{e (m+1)}+\frac{B d x^{2 n+1} (e x)^m}{m+2 n+1}","\frac{x^{n+1} (e x)^m (A d+B c)}{m+n+1}+\frac{A c (e x)^{m+1}}{e (m+1)}+\frac{B d x^{2 n+1} (e x)^m}{m+2 n+1}",1,"((B*c + A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (B*d*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + (A*c*(e*x)^(1 + m))/(e*(1 + m))","A",6,3,20,0.1500,1,"{448, 20, 30}"
5,1,120,0,0.1197266,"\int \frac{(e x)^m \left(A+B x^n\right) \left(c+d x^n\right)}{a+b x^n} \, dx","Int[((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n),x]","\frac{(e x)^{m+1} (A b-a B) (b c-a d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a b^2 e (m+1)}+\frac{(e x)^{m+1} (-a B d+A b d+b B c)}{b^2 e (m+1)}+\frac{B d x^{n+1} (e x)^m}{b (m+n+1)}","\frac{(e x)^{m+1} (A b-a B) (b c-a d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a b^2 e (m+1)}+\frac{(e x)^{m+1} (-a B d+A b d+b B c)}{b^2 e (m+1)}+\frac{B d x^{n+1} (e x)^m}{b (m+n+1)}",1,"(B*d*x^(1 + n)*(e*x)^m)/(b*(1 + m + n)) + ((b*B*c + A*b*d - a*B*d)*(e*x)^(1 + m))/(b^2*e*(1 + m)) + ((A*b - a*B)*(b*c - a*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*b^2*e*(1 + m))","A",5,4,29,0.1379,1,"{570, 20, 30, 364}"
6,1,177,0,0.2581428,"\int \frac{(e x)^m \left(A+B x^n\right) \left(c+d x^n\right)}{\left(a+b x^n\right)^2} \, dx","Int[((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n)^2,x]","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (b c (a B (m+1)-A b (m-n+1))+a d (A b (m+1)-a B (m+n+1)))}{a^2 b^2 e (m+1) n}-\frac{d (e x)^{m+1} (A b (m+1)-a B (m+n+1))}{a b^2 e (m+1) n}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)}{a b e n \left(a+b x^n\right)}","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (b c (a B (m+1)-A b (m-n+1))+a d (A b (m+1)-a B (m+n+1)))}{a^2 b^2 e (m+1) n}-\frac{d (e x)^{m+1} (A b (m+1)-a B (m+n+1))}{a b^2 e (m+1) n}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)}{a b e n \left(a+b x^n\right)}",1,"-((d*(A*b*(1 + m) - a*B*(1 + m + n))*(e*x)^(1 + m))/(a*b^2*e*(1 + m)*n)) + ((A*b - a*B)*(e*x)^(1 + m)*(c + d*x^n))/(a*b*e*n*(a + b*x^n)) + ((b*c*(a*B*(1 + m) - A*b*(1 + m - n)) + a*d*(A*b*(1 + m) - a*B*(1 + m + n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*b^2*e*(1 + m)*n)","A",3,3,29,0.1034,1,"{594, 459, 364}"
7,1,228,0,0.2729376,"\int \frac{(e x)^m \left(A+B x^n\right) \left(c+d x^n\right)}{\left(a+b x^n\right)^3} \, dx","Int[((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n)^3,x]","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (b c (m-n+1) (a B (m+1)-A b (m-2 n+1))+a d (m+1) (A b (m-n+1)-a B (m+n+1)))}{2 a^3 b^2 e (m+1) n^2}-\frac{(e x)^{m+1} (A b (b c (m-2 n+1)-a d (m-n+1))-a B (b c (m+1)-a d (m+n+1)))}{2 a^2 b^2 e n^2 \left(a+b x^n\right)}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)}{2 a b e n \left(a+b x^n\right)^2}","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (b c (m-n+1) (a B (m+1)-A b (m-2 n+1))+a d (m+1) (A b (m-n+1)-a B (m+n+1)))}{2 a^3 b^2 e (m+1) n^2}-\frac{(e x)^{m+1} (A b (b c (m-2 n+1)-a d (m-n+1))-a B (b c (m+1)-a d (m+n+1)))}{2 a^2 b^2 e n^2 \left(a+b x^n\right)}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)}{2 a b e n \left(a+b x^n\right)^2}",1,"-((A*b*(b*c*(1 + m - 2*n) - a*d*(1 + m - n)) - a*B*(b*c*(1 + m) - a*d*(1 + m + n)))*(e*x)^(1 + m))/(2*a^2*b^2*e*n^2*(a + b*x^n)) + ((A*b - a*B)*(e*x)^(1 + m)*(c + d*x^n))/(2*a*b*e*n*(a + b*x^n)^2) - ((b*c*(a*B*(1 + m) - A*b*(1 + m - 2*n))*(1 + m - n) + a*d*(1 + m)*(A*b*(1 + m - n) - a*B*(1 + m + n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(2*a^3*b^2*e*(1 + m)*n^2)","A",3,3,29,0.1034,1,"{594, 457, 364}"
8,1,318,0,0.4111826,"\int (e x)^m \left(a+b x^n\right)^3 \left(A+B x^n\right) \left(c+d x^n\right)^2 \, dx","Int[(e*x)^m*(a + b*x^n)^3*(A + B*x^n)*(c + d*x^n)^2,x]","\frac{a x^{2 n+1} (e x)^m \left(A \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+a B c (2 a d+3 b c)\right)}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left(A b \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a B \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)\right)}{m+3 n+1}+\frac{b x^{4 n+1} (e x)^m \left(3 a^2 B d^2+3 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{m+4 n+1}+\frac{a^2 c x^{n+1} (e x)^m (2 a A d+a B c+3 A b c)}{m+n+1}+\frac{a^3 A c^2 (e x)^{m+1}}{e (m+1)}+\frac{b^2 d x^{5 n+1} (e x)^m (3 a B d+A b d+2 b B c)}{m+5 n+1}+\frac{b^3 B d^2 x^{6 n+1} (e x)^m}{m+6 n+1}","\frac{a x^{2 n+1} (e x)^m \left(A \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+a B c (2 a d+3 b c)\right)}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left(A b \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a B \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)\right)}{m+3 n+1}+\frac{b x^{4 n+1} (e x)^m \left(3 a^2 B d^2+3 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{m+4 n+1}+\frac{a^2 c x^{n+1} (e x)^m (2 a A d+a B c+3 A b c)}{m+n+1}+\frac{a^3 A c^2 (e x)^{m+1}}{e (m+1)}+\frac{b^2 d x^{5 n+1} (e x)^m (3 a B d+A b d+2 b B c)}{m+5 n+1}+\frac{b^3 B d^2 x^{6 n+1} (e x)^m}{m+6 n+1}",1,"(a^2*c*(3*A*b*c + a*B*c + 2*a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (a*(a*B*c*(3*b*c + 2*a*d) + A*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + ((a*B*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2) + A*b*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2))*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (b*(3*a^2*B*d^2 + 3*a*b*d*(2*B*c + A*d) + b^2*c*(B*c + 2*A*d))*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (b^2*d*(2*b*B*c + A*b*d + 3*a*B*d)*x^(1 + 5*n)*(e*x)^m)/(1 + m + 5*n) + (b^3*B*d^2*x^(1 + 6*n)*(e*x)^m)/(1 + m + 6*n) + (a^3*A*c^2*(e*x)^(1 + m))/(e*(1 + m))","A",14,3,31,0.09677,1,"{570, 20, 30}"
9,1,237,0,0.310404,"\int (e x)^m \left(a+b x^n\right)^2 \left(A+B x^n\right) \left(c+d x^n\right)^2 \, dx","Int[(e*x)^m*(a + b*x^n)^2*(A + B*x^n)*(c + d*x^n)^2,x]","\frac{x^{2 n+1} (e x)^m \left(A \left(a^2 d^2+4 a b c d+b^2 c^2\right)+2 a B c (a d+b c)\right)}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left(a^2 B d^2+2 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{m+3 n+1}+\frac{a^2 A c^2 (e x)^{m+1}}{e (m+1)}+\frac{a c x^{n+1} (e x)^m (2 A (a d+b c)+a B c)}{m+n+1}+\frac{b d x^{4 n+1} (e x)^m (2 a B d+A b d+2 b B c)}{m+4 n+1}+\frac{b^2 B d^2 x^{5 n+1} (e x)^m}{m+5 n+1}","\frac{x^{2 n+1} (e x)^m \left(A \left(a^2 d^2+4 a b c d+b^2 c^2\right)+2 a B c (a d+b c)\right)}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left(a^2 B d^2+2 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{m+3 n+1}+\frac{a^2 A c^2 (e x)^{m+1}}{e (m+1)}+\frac{a c x^{n+1} (e x)^m (2 A (a d+b c)+a B c)}{m+n+1}+\frac{b d x^{4 n+1} (e x)^m (2 a B d+A b d+2 b B c)}{m+4 n+1}+\frac{b^2 B d^2 x^{5 n+1} (e x)^m}{m+5 n+1}",1,"(a*c*(a*B*c + 2*A*(b*c + a*d))*x^(1 + n)*(e*x)^m)/(1 + m + n) + ((2*a*B*c*(b*c + a*d) + A*(b^2*c^2 + 4*a*b*c*d + a^2*d^2))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + ((a^2*B*d^2 + 2*a*b*d*(2*B*c + A*d) + b^2*c*(B*c + 2*A*d))*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (b*d*(2*b*B*c + A*b*d + 2*a*B*d)*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (b^2*B*d^2*x^(1 + 5*n)*(e*x)^m)/(1 + m + 5*n) + (a^2*A*c^2*(e*x)^(1 + m))/(e*(1 + m))","A",12,3,31,0.09677,1,"{570, 20, 30}"
10,1,160,0,0.1715055,"\int (e x)^m \left(a+b x^n\right) \left(A+B x^n\right) \left(c+d x^n\right)^2 \, dx","Int[(e*x)^m*(a + b*x^n)*(A + B*x^n)*(c + d*x^n)^2,x]","\frac{c x^{n+1} (e x)^m (2 a A d+a B c+A b c)}{m+n+1}+\frac{x^{2 n+1} (e x)^m (a d (A d+2 B c)+b c (2 A d+B c))}{m+2 n+1}+\frac{d x^{3 n+1} (e x)^m (a B d+A b d+2 b B c)}{m+3 n+1}+\frac{a A c^2 (e x)^{m+1}}{e (m+1)}+\frac{b B d^2 x^{4 n+1} (e x)^m}{m+4 n+1}","\frac{c x^{n+1} (e x)^m (2 a A d+a B c+A b c)}{m+n+1}+\frac{x^{2 n+1} (e x)^m (a d (A d+2 B c)+b c (2 A d+B c))}{m+2 n+1}+\frac{d x^{3 n+1} (e x)^m (a B d+A b d+2 b B c)}{m+3 n+1}+\frac{a A c^2 (e x)^{m+1}}{e (m+1)}+\frac{b B d^2 x^{4 n+1} (e x)^m}{m+4 n+1}",1,"(c*(A*b*c + a*B*c + 2*a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + ((a*d*(2*B*c + A*d) + b*c*(B*c + 2*A*d))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + (d*(2*b*B*c + A*b*d + a*B*d)*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (b*B*d^2*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (a*A*c^2*(e*x)^(1 + m))/(e*(1 + m))","A",10,3,29,0.1034,1,"{570, 20, 30}"
11,1,102,0,0.0759361,"\int (e x)^m \left(A+B x^n\right) \left(c+d x^n\right)^2 \, dx","Int[(e*x)^m*(A + B*x^n)*(c + d*x^n)^2,x]","\frac{c x^{n+1} (e x)^m (2 A d+B c)}{m+n+1}+\frac{d x^{2 n+1} (e x)^m (A d+2 B c)}{m+2 n+1}+\frac{A c^2 (e x)^{m+1}}{e (m+1)}+\frac{B d^2 x^{3 n+1} (e x)^m}{m+3 n+1}","\frac{c x^{n+1} (e x)^m (2 A d+B c)}{m+n+1}+\frac{d x^{2 n+1} (e x)^m (A d+2 B c)}{m+2 n+1}+\frac{A c^2 (e x)^{m+1}}{e (m+1)}+\frac{B d^2 x^{3 n+1} (e x)^m}{m+3 n+1}",1,"(c*(B*c + 2*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (d*(2*B*c + A*d)*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + (B*d^2*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (A*c^2*(e*x)^(1 + m))/(e*(1 + m))","A",8,3,22,0.1364,1,"{448, 20, 30}"
12,1,185,0,0.2257003,"\int \frac{(e x)^m \left(A+B x^n\right) \left(c+d x^n\right)^2}{a+b x^n} \, dx","Int[((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n),x]","\frac{(e x)^{m+1} \left(a^2 B d^2-a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{b^3 e (m+1)}+\frac{(e x)^{m+1} (A b-a B) (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a b^3 e (m+1)}+\frac{d x^{n+1} (e x)^m (-a B d+A b d+2 b B c)}{b^2 (m+n+1)}+\frac{B d^2 x^{2 n+1} (e x)^m}{b (m+2 n+1)}","\frac{(e x)^{m+1} \left(a^2 B d^2-a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{b^3 e (m+1)}+\frac{(e x)^{m+1} (A b-a B) (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a b^3 e (m+1)}+\frac{d x^{n+1} (e x)^m (-a B d+A b d+2 b B c)}{b^2 (m+n+1)}+\frac{B d^2 x^{2 n+1} (e x)^m}{b (m+2 n+1)}",1,"(d*(2*b*B*c + A*b*d - a*B*d)*x^(1 + n)*(e*x)^m)/(b^2*(1 + m + n)) + (B*d^2*x^(1 + 2*n)*(e*x)^m)/(b*(1 + m + 2*n)) + ((a^2*B*d^2 - a*b*d*(2*B*c + A*d) + b^2*c*(B*c + 2*A*d))*(e*x)^(1 + m))/(b^3*e*(1 + m)) + ((A*b - a*B)*(b*c - a*d)^2*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*b^3*e*(1 + m))","A",7,4,31,0.1290,1,"{570, 20, 30, 364}"
13,1,268,0,0.6687068,"\int \frac{(e x)^m \left(A+B x^n\right) \left(c+d x^n\right)^2}{\left(a+b x^n\right)^2} \, dx","Int[((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n)^2,x]","-\frac{(e x)^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (b c (m-n+1)-a d (m+n+1))-a B (b c (m+1)-a d (m+2 n+1)))}{a^2 b^3 e (m+1) n}-\frac{d (e x)^{m+1} (A b (2 b c (m+1)-a d (m+n+1))-a B (2 b c (m+n+1)-a d (m+2 n+1)))}{a b^3 e (m+1) n}-\frac{d^2 x^{n+1} (e x)^m (A b (m+n+1)-a B (m+2 n+1))}{a b^2 n (m+n+1)}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)^2}{a b e n \left(a+b x^n\right)}","-\frac{(e x)^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (b c (m-n+1)-a d (m+n+1))-a B (b c (m+1)-a d (m+2 n+1)))}{a^2 b^3 e (m+1) n}-\frac{d (e x)^{m+1} (A b (2 b c (m+1)-a d (m+n+1))-a B (2 b c (m+n+1)-a d (m+2 n+1)))}{a b^3 e (m+1) n}-\frac{d^2 x^{n+1} (e x)^m (A b (m+n+1)-a B (m+2 n+1))}{a b^2 n (m+n+1)}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)^2}{a b e n \left(a+b x^n\right)}",1,"-((d^2*(A*b*(1 + m + n) - a*B*(1 + m + 2*n))*x^(1 + n)*(e*x)^m)/(a*b^2*n*(1 + m + n))) - (d*(A*b*(2*b*c*(1 + m) - a*d*(1 + m + n)) - a*B*(2*b*c*(1 + m + n) - a*d*(1 + m + 2*n)))*(e*x)^(1 + m))/(a*b^3*e*(1 + m)*n) + ((A*b - a*B)*(e*x)^(1 + m)*(c + d*x^n)^2)/(a*b*e*n*(a + b*x^n)) - ((b*c - a*d)*(A*b*(b*c*(1 + m - n) - a*d*(1 + m + n)) - a*B*(b*c*(1 + m) - a*d*(1 + m + 2*n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*b^3*e*(1 + m)*n)","A",6,5,31,0.1613,1,"{594, 570, 20, 30, 364}"
14,1,322,0,0.5435984,"\int \frac{(e x)^m \left(A+B x^n\right) \left(c+d x^n\right)^2}{\left(a+b x^n\right)^3} \, dx","Int[((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n)^3,x]","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (b c (a B (m+1)-A b (m-2 n+1)) (a d (m+1)-b c (m-n+1))-a d (A b (m+1)-a B (m+2 n+1)) (b c (m+1)-a d (m+n+1)))}{2 a^3 b^3 e (m+1) n^2}+\frac{(e x)^{m+1} (b c-a d) \left(c (a B (m+1)-A b (m-2 n+1))-d x^n (A b (m+1)-a B (m+2 n+1))\right)}{2 a^2 b^2 e n^2 \left(a+b x^n\right)}+\frac{d (e x)^{m+1} (A b (m+1)-a B (m+2 n+1)) (b c (m+1)-a d (m+n+1))}{2 a^2 b^3 e (m+1) n^2}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)^2}{2 a b e n \left(a+b x^n\right)^2}","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (b c (a B (m+1)-A b (m-2 n+1)) (a d (m+1)-b c (m-n+1))-a d (A b (m+1)-a B (m+2 n+1)) (b c (m+1)-a d (m+n+1)))}{2 a^3 b^3 e (m+1) n^2}+\frac{(e x)^{m+1} (b c-a d) \left(c (a B (m+1)-A b (m-2 n+1))-d x^n (A b (m+1)-a B (m+2 n+1))\right)}{2 a^2 b^2 e n^2 \left(a+b x^n\right)}+\frac{d (e x)^{m+1} (A b (m+1)-a B (m+2 n+1)) (b c (m+1)-a d (m+n+1))}{2 a^2 b^3 e (m+1) n^2}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)^2}{2 a b e n \left(a+b x^n\right)^2}",1,"(d*(b*c*(1 + m) - a*d*(1 + m + n))*(A*b*(1 + m) - a*B*(1 + m + 2*n))*(e*x)^(1 + m))/(2*a^2*b^3*e*(1 + m)*n^2) + ((A*b - a*B)*(e*x)^(1 + m)*(c + d*x^n)^2)/(2*a*b*e*n*(a + b*x^n)^2) + ((b*c - a*d)*(e*x)^(1 + m)*(c*(a*B*(1 + m) - A*b*(1 + m - 2*n)) - d*(A*b*(1 + m) - a*B*(1 + m + 2*n))*x^n))/(2*a^2*b^2*e*n^2*(a + b*x^n)) + ((b*c*(a*B*(1 + m) - A*b*(1 + m - 2*n))*(a*d*(1 + m) - b*c*(1 + m - n)) - a*d*(b*c*(1 + m) - a*d*(1 + m + n))*(A*b*(1 + m) - a*B*(1 + m + 2*n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(2*a^3*b^3*e*(1 + m)*n^2)","A",4,3,31,0.09677,1,"{594, 459, 364}"
15,1,410,0,0.6244603,"\int (e x)^m \left(a+b x^n\right)^3 \left(A+B x^n\right) \left(c+d x^n\right)^3 \, dx","Int[(e*x)^m*(a + b*x^n)^3*(A + B*x^n)*(c + d*x^n)^3,x]","\frac{3 a c x^{2 n+1} (e x)^m \left(A \left(a^2 d^2+3 a b c d+b^2 c^2\right)+a B c (a d+b c)\right)}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left(A \left(9 a^2 b c d^2+a^3 d^3+9 a b^2 c^2 d+b^3 c^3\right)+3 a B c \left(a^2 d^2+3 a b c d+b^2 c^2\right)\right)}{m+3 n+1}+\frac{x^{4 n+1} (e x)^m \left(3 a^2 b d^2 (A d+3 B c)+a^3 B d^3+9 a b^2 c d (A d+B c)+b^3 c^2 (3 A d+B c)\right)}{m+4 n+1}+\frac{3 b d x^{5 n+1} (e x)^m \left(a^2 B d^2+a b d (A d+3 B c)+b^2 c (A d+B c)\right)}{m+5 n+1}+\frac{a^2 c^2 x^{n+1} (e x)^m (3 A (a d+b c)+a B c)}{m+n+1}+\frac{a^3 A c^3 (e x)^{m+1}}{e (m+1)}+\frac{b^2 d^2 x^{6 n+1} (e x)^m (3 a B d+A b d+3 b B c)}{m+6 n+1}+\frac{b^3 B d^3 x^{7 n+1} (e x)^m}{m+7 n+1}","\frac{3 a c x^{2 n+1} (e x)^m \left(A \left(a^2 d^2+3 a b c d+b^2 c^2\right)+a B c (a d+b c)\right)}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left(A \left(9 a^2 b c d^2+a^3 d^3+9 a b^2 c^2 d+b^3 c^3\right)+3 a B c \left(a^2 d^2+3 a b c d+b^2 c^2\right)\right)}{m+3 n+1}+\frac{x^{4 n+1} (e x)^m \left(3 a^2 b d^2 (A d+3 B c)+a^3 B d^3+9 a b^2 c d (A d+B c)+b^3 c^2 (3 A d+B c)\right)}{m+4 n+1}+\frac{3 b d x^{5 n+1} (e x)^m \left(a^2 B d^2+a b d (A d+3 B c)+b^2 c (A d+B c)\right)}{m+5 n+1}+\frac{a^2 c^2 x^{n+1} (e x)^m (3 A (a d+b c)+a B c)}{m+n+1}+\frac{a^3 A c^3 (e x)^{m+1}}{e (m+1)}+\frac{b^2 d^2 x^{6 n+1} (e x)^m (3 a B d+A b d+3 b B c)}{m+6 n+1}+\frac{b^3 B d^3 x^{7 n+1} (e x)^m}{m+7 n+1}",1,"(a^2*c^2*(a*B*c + 3*A*(b*c + a*d))*x^(1 + n)*(e*x)^m)/(1 + m + n) + (3*a*c*(a*B*c*(b*c + a*d) + A*(b^2*c^2 + 3*a*b*c*d + a^2*d^2))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + ((3*a*B*c*(b^2*c^2 + 3*a*b*c*d + a^2*d^2) + A*(b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3))*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + ((a^3*B*d^3 + 9*a*b^2*c*d*(B*c + A*d) + 3*a^2*b*d^2*(3*B*c + A*d) + b^3*c^2*(B*c + 3*A*d))*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (3*b*d*(a^2*B*d^2 + b^2*c*(B*c + A*d) + a*b*d*(3*B*c + A*d))*x^(1 + 5*n)*(e*x)^m)/(1 + m + 5*n) + (b^2*d^2*(3*b*B*c + A*b*d + 3*a*B*d)*x^(1 + 6*n)*(e*x)^m)/(1 + m + 6*n) + (b^3*B*d^3*x^(1 + 7*n)*(e*x)^m)/(1 + m + 7*n) + (a^3*A*c^3*(e*x)^(1 + m))/(e*(1 + m))","A",16,3,31,0.09677,1,"{570, 20, 30}"
16,1,310,0,0.4139029,"\int (e x)^m \left(a+b x^n\right)^2 \left(A+B x^n\right) \left(c+d x^n\right)^3 \, dx","Int[(e*x)^m*(a + b*x^n)^2*(A + B*x^n)*(c + d*x^n)^3,x]","\frac{c x^{2 n+1} (e x)^m \left(A \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a B c (3 a d+2 b c)\right)}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left(a^2 d^2 (A d+3 B c)+6 a b c d (A d+B c)+b^2 c^2 (3 A d+B c)\right)}{m+3 n+1}+\frac{d x^{4 n+1} (e x)^m \left(a^2 B d^2+2 a b d (A d+3 B c)+3 b^2 c (A d+B c)\right)}{m+4 n+1}+\frac{a^2 A c^3 (e x)^{m+1}}{e (m+1)}+\frac{a c^2 x^{n+1} (e x)^m (3 a A d+a B c+2 A b c)}{m+n+1}+\frac{b d^2 x^{5 n+1} (e x)^m (2 a B d+A b d+3 b B c)}{m+5 n+1}+\frac{b^2 B d^3 x^{6 n+1} (e x)^m}{m+6 n+1}","\frac{c x^{2 n+1} (e x)^m \left(A \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a B c (3 a d+2 b c)\right)}{m+2 n+1}+\frac{x^{3 n+1} (e x)^m \left(a^2 d^2 (A d+3 B c)+6 a b c d (A d+B c)+b^2 c^2 (3 A d+B c)\right)}{m+3 n+1}+\frac{d x^{4 n+1} (e x)^m \left(a^2 B d^2+2 a b d (A d+3 B c)+3 b^2 c (A d+B c)\right)}{m+4 n+1}+\frac{a^2 A c^3 (e x)^{m+1}}{e (m+1)}+\frac{a c^2 x^{n+1} (e x)^m (3 a A d+a B c+2 A b c)}{m+n+1}+\frac{b d^2 x^{5 n+1} (e x)^m (2 a B d+A b d+3 b B c)}{m+5 n+1}+\frac{b^2 B d^3 x^{6 n+1} (e x)^m}{m+6 n+1}",1,"(a*c^2*(2*A*b*c + a*B*c + 3*a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (c*(a*B*c*(2*b*c + 3*a*d) + A*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + ((6*a*b*c*d*(B*c + A*d) + a^2*d^2*(3*B*c + A*d) + b^2*c^2*(B*c + 3*A*d))*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (d*(a^2*B*d^2 + 3*b^2*c*(B*c + A*d) + 2*a*b*d*(3*B*c + A*d))*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (b*d^2*(3*b*B*c + A*b*d + 2*a*B*d)*x^(1 + 5*n)*(e*x)^m)/(1 + m + 5*n) + (b^2*B*d^3*x^(1 + 6*n)*(e*x)^m)/(1 + m + 6*n) + (a^2*A*c^3*(e*x)^(1 + m))/(e*(1 + m))","A",14,3,31,0.09677,1,"{570, 20, 30}"
17,1,210,0,0.2581279,"\int (e x)^m \left(a+b x^n\right) \left(A+B x^n\right) \left(c+d x^n\right)^3 \, dx","Int[(e*x)^m*(a + b*x^n)*(A + B*x^n)*(c + d*x^n)^3,x]","\frac{c^2 x^{n+1} (e x)^m (3 a A d+a B c+A b c)}{m+n+1}+\frac{d^2 x^{4 n+1} (e x)^m (a B d+A b d+3 b B c)}{m+4 n+1}+\frac{c x^{2 n+1} (e x)^m (3 a d (A d+B c)+b c (3 A d+B c))}{m+2 n+1}+\frac{d x^{3 n+1} (e x)^m (a d (A d+3 B c)+3 b c (A d+B c))}{m+3 n+1}+\frac{a A c^3 (e x)^{m+1}}{e (m+1)}+\frac{b B d^3 x^{5 n+1} (e x)^m}{m+5 n+1}","\frac{c^2 x^{n+1} (e x)^m (3 a A d+a B c+A b c)}{m+n+1}+\frac{d^2 x^{4 n+1} (e x)^m (a B d+A b d+3 b B c)}{m+4 n+1}+\frac{c x^{2 n+1} (e x)^m (3 a d (A d+B c)+b c (3 A d+B c))}{m+2 n+1}+\frac{d x^{3 n+1} (e x)^m (a d (A d+3 B c)+3 b c (A d+B c))}{m+3 n+1}+\frac{a A c^3 (e x)^{m+1}}{e (m+1)}+\frac{b B d^3 x^{5 n+1} (e x)^m}{m+5 n+1}",1,"(c^2*(A*b*c + a*B*c + 3*a*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (c*(3*a*d*(B*c + A*d) + b*c*(B*c + 3*A*d))*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + (d*(3*b*c*(B*c + A*d) + a*d*(3*B*c + A*d))*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (d^2*(3*b*B*c + A*b*d + a*B*d)*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (b*B*d^3*x^(1 + 5*n)*(e*x)^m)/(1 + m + 5*n) + (a*A*c^3*(e*x)^(1 + m))/(e*(1 + m))","A",12,3,29,0.1034,1,"{570, 20, 30}"
18,1,137,0,0.1107534,"\int (e x)^m \left(A+B x^n\right) \left(c+d x^n\right)^3 \, dx","Int[(e*x)^m*(A + B*x^n)*(c + d*x^n)^3,x]","\frac{c^2 x^{n+1} (e x)^m (3 A d+B c)}{m+n+1}+\frac{d^2 x^{3 n+1} (e x)^m (A d+3 B c)}{m+3 n+1}+\frac{3 c d x^{2 n+1} (e x)^m (A d+B c)}{m+2 n+1}+\frac{A c^3 (e x)^{m+1}}{e (m+1)}+\frac{B d^3 x^{4 n+1} (e x)^m}{m+4 n+1}","\frac{c^2 x^{n+1} (e x)^m (3 A d+B c)}{m+n+1}+\frac{d^2 x^{3 n+1} (e x)^m (A d+3 B c)}{m+3 n+1}+\frac{3 c d x^{2 n+1} (e x)^m (A d+B c)}{m+2 n+1}+\frac{A c^3 (e x)^{m+1}}{e (m+1)}+\frac{B d^3 x^{4 n+1} (e x)^m}{m+4 n+1}",1,"(c^2*(B*c + 3*A*d)*x^(1 + n)*(e*x)^m)/(1 + m + n) + (3*c*d*(B*c + A*d)*x^(1 + 2*n)*(e*x)^m)/(1 + m + 2*n) + (d^2*(3*B*c + A*d)*x^(1 + 3*n)*(e*x)^m)/(1 + m + 3*n) + (B*d^3*x^(1 + 4*n)*(e*x)^m)/(1 + m + 4*n) + (A*c^3*(e*x)^(1 + m))/(e*(1 + m))","A",10,3,22,0.1364,1,"{448, 20, 30}"
19,1,270,0,0.3891382,"\int \frac{(e x)^m \left(A+B x^n\right) \left(c+d x^n\right)^3}{a+b x^n} \, dx","Int[((e*x)^m*(A + B*x^n)*(c + d*x^n)^3)/(a + b*x^n),x]","-\frac{(e x)^{m+1} \left(-a^2 b d^2 (A d+3 B c)+a^3 B d^3+3 a b^2 c d (A d+B c)+b^3 \left(-c^2\right) (3 A d+B c)\right)}{b^4 e (m+1)}+\frac{d x^{n+1} (e x)^m \left(a^2 B d^2-a b d (A d+3 B c)+3 b^2 c (A d+B c)\right)}{b^3 (m+n+1)}+\frac{d^2 x^{2 n+1} (e x)^m (-a B d+A b d+3 b B c)}{b^2 (m+2 n+1)}+\frac{(e x)^{m+1} (A b-a B) (b c-a d)^3 \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a b^4 e (m+1)}+\frac{B d^3 x^{3 n+1} (e x)^m}{b (m+3 n+1)}","-\frac{(e x)^{m+1} \left(-a^2 b d^2 (A d+3 B c)+a^3 B d^3+3 a b^2 c d (A d+B c)+b^3 \left(-c^2\right) (3 A d+B c)\right)}{b^4 e (m+1)}+\frac{d x^{n+1} (e x)^m \left(a^2 B d^2-a b d (A d+3 B c)+3 b^2 c (A d+B c)\right)}{b^3 (m+n+1)}+\frac{d^2 x^{2 n+1} (e x)^m (-a B d+A b d+3 b B c)}{b^2 (m+2 n+1)}+\frac{(e x)^{m+1} (A b-a B) (b c-a d)^3 \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a b^4 e (m+1)}+\frac{B d^3 x^{3 n+1} (e x)^m}{b (m+3 n+1)}",1,"(d*(a^2*B*d^2 + 3*b^2*c*(B*c + A*d) - a*b*d*(3*B*c + A*d))*x^(1 + n)*(e*x)^m)/(b^3*(1 + m + n)) + (d^2*(3*b*B*c + A*b*d - a*B*d)*x^(1 + 2*n)*(e*x)^m)/(b^2*(1 + m + 2*n)) + (B*d^3*x^(1 + 3*n)*(e*x)^m)/(b*(1 + m + 3*n)) - ((a^3*B*d^3 + 3*a*b^2*c*d*(B*c + A*d) - a^2*b*d^2*(3*B*c + A*d) - b^3*c^2*(B*c + 3*A*d))*(e*x)^(1 + m))/(b^4*e*(1 + m)) + ((A*b - a*B)*(b*c - a*d)^3*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*b^4*e*(1 + m))","A",9,4,31,0.1290,1,"{570, 20, 30, 364}"
20,1,389,0,1.0237213,"\int \frac{(e x)^m \left(A+B x^n\right) \left(c+d x^n\right)^3}{\left(a+b x^n\right)^2} \, dx","Int[((e*x)^m*(A + B*x^n)*(c + d*x^n)^3)/(a + b*x^n)^2,x]","-\frac{d (e x)^{m+1} \left(A b \left(a^2 d^2 (m+2 n+1)-3 a b c d (m+n+1)+3 b^2 c^2 (m+1)\right)-a B \left(a^2 d^2 (m+3 n+1)-3 a b c d (m+2 n+1)+3 b^2 c^2 (m+n+1)\right)\right)}{a b^4 e (m+1) n}-\frac{(e x)^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (b c (m-n+1)-a d (m+2 n+1))-a B (b c (m+1)-a d (m+3 n+1)))}{a^2 b^4 e (m+1) n}-\frac{d^2 x^{n+1} (e x)^m (A b (3 b c (m+n+1)-a d (m+2 n+1))-a B (3 b c (m+2 n+1)-a d (m+3 n+1)))}{a b^3 n (m+n+1)}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)^3}{a b e n \left(a+b x^n\right)}-\frac{d^3 x^{2 n+1} (e x)^m \left(A-\frac{a B (m+3 n+1)}{b (m+2 n+1)}\right)}{a b n}","-\frac{d (e x)^{m+1} \left(A b \left(a^2 d^2 (m+2 n+1)-3 a b c d (m+n+1)+3 b^2 c^2 (m+1)\right)-a B \left(a^2 d^2 (m+3 n+1)-3 a b c d (m+2 n+1)+3 b^2 c^2 (m+n+1)\right)\right)}{a b^4 e (m+1) n}-\frac{(e x)^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (b c (m-n+1)-a d (m+2 n+1))-a B (b c (m+1)-a d (m+3 n+1)))}{a^2 b^4 e (m+1) n}-\frac{d^2 x^{n+1} (e x)^m (A b (3 b c (m+n+1)-a d (m+2 n+1))-a B (3 b c (m+2 n+1)-a d (m+3 n+1)))}{a b^3 n (m+n+1)}-\frac{d^3 x^{2 n+1} (e x)^m (A b (m+2 n+1)-a B (m+3 n+1))}{a b^2 n (m+2 n+1)}+\frac{(e x)^{m+1} (A b-a B) \left(c+d x^n\right)^3}{a b e n \left(a+b x^n\right)}",1,"-((d^2*(A*b*(3*b*c*(1 + m + n) - a*d*(1 + m + 2*n)) - a*B*(3*b*c*(1 + m + 2*n) - a*d*(1 + m + 3*n)))*x^(1 + n)*(e*x)^m)/(a*b^3*n*(1 + m + n))) - (d^3*(A - (a*B*(1 + m + 3*n))/(b*(1 + m + 2*n)))*x^(1 + 2*n)*(e*x)^m)/(a*b*n) - (d*(A*b*(3*b^2*c^2*(1 + m) - 3*a*b*c*d*(1 + m + n) + a^2*d^2*(1 + m + 2*n)) - a*B*(3*b^2*c^2*(1 + m + n) - 3*a*b*c*d*(1 + m + 2*n) + a^2*d^2*(1 + m + 3*n)))*(e*x)^(1 + m))/(a*b^4*e*(1 + m)*n) + ((A*b - a*B)*(e*x)^(1 + m)*(c + d*x^n)^3)/(a*b*e*n*(a + b*x^n)) - ((b*c - a*d)^2*(A*b*(b*c*(1 + m - n) - a*d*(1 + m + 2*n)) - a*B*(b*c*(1 + m) - a*d*(1 + m + 3*n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*b^4*e*(1 + m)*n)","A",8,5,31,0.1613,1,"{594, 570, 20, 30, 364}"
21,1,380,0,0.6210508,"\int \frac{(e x)^m \left(a+b x^n\right)^4 \left(A+B x^n\right)}{c+d x^n} \, dx","Int[((e*x)^m*(a + b*x^n)^4*(A + B*x^n))/(c + d*x^n),x]","\frac{b x^{n+1} (e x)^m \left(-6 a^2 b d^2 (B c-A d)+4 a^3 B d^3+4 a b^2 c d (B c-A d)+b^3 \left(-c^2\right) (B c-A d)\right)}{d^4 (m+n+1)}+\frac{(e x)^{m+1} \left(6 a^2 b^2 c d^2 (B c-A d)-4 a^3 b d^3 (B c-A d)+a^4 B d^4-4 a b^3 c^2 d (B c-A d)+b^4 c^3 (B c-A d)\right)}{d^5 e (m+1)}+\frac{b^2 x^{2 n+1} (e x)^m \left(6 a^2 B d^2-4 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 (m+2 n+1)}-\frac{b^3 x^{3 n+1} (e x)^m (-4 a B d-A b d+b B c)}{d^2 (m+3 n+1)}-\frac{(e x)^{m+1} (b c-a d)^4 (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d^5 e (m+1)}+\frac{b^4 B x^{4 n+1} (e x)^m}{d (m+4 n+1)}","\frac{b x^{n+1} (e x)^m \left(-6 a^2 b d^2 (B c-A d)+4 a^3 B d^3+4 a b^2 c d (B c-A d)+b^3 \left(-c^2\right) (B c-A d)\right)}{d^4 (m+n+1)}+\frac{(e x)^{m+1} \left(6 a^2 b^2 c d^2 (B c-A d)-4 a^3 b d^3 (B c-A d)+a^4 B d^4-4 a b^3 c^2 d (B c-A d)+b^4 c^3 (B c-A d)\right)}{d^5 e (m+1)}+\frac{b^2 x^{2 n+1} (e x)^m \left(6 a^2 B d^2-4 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 (m+2 n+1)}-\frac{b^3 x^{3 n+1} (e x)^m (-4 a B d-A b d+b B c)}{d^2 (m+3 n+1)}-\frac{(e x)^{m+1} (b c-a d)^4 (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d^5 e (m+1)}+\frac{b^4 B x^{4 n+1} (e x)^m}{d (m+4 n+1)}",1,"(b*(4*a^3*B*d^3 - b^3*c^2*(B*c - A*d) + 4*a*b^2*c*d*(B*c - A*d) - 6*a^2*b*d^2*(B*c - A*d))*x^(1 + n)*(e*x)^m)/(d^4*(1 + m + n)) + (b^2*(6*a^2*B*d^2 + b^2*c*(B*c - A*d) - 4*a*b*d*(B*c - A*d))*x^(1 + 2*n)*(e*x)^m)/(d^3*(1 + m + 2*n)) - (b^3*(b*B*c - A*b*d - 4*a*B*d)*x^(1 + 3*n)*(e*x)^m)/(d^2*(1 + m + 3*n)) + (b^4*B*x^(1 + 4*n)*(e*x)^m)/(d*(1 + m + 4*n)) + ((a^4*B*d^4 + b^4*c^3*(B*c - A*d) - 4*a*b^3*c^2*d*(B*c - A*d) + 6*a^2*b^2*c*d^2*(B*c - A*d) - 4*a^3*b*d^3*(B*c - A*d))*(e*x)^(1 + m))/(d^5*e*(1 + m)) - ((b*c - a*d)^4*(B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*d^5*e*(1 + m))","A",11,4,31,0.1290,1,"{570, 20, 30, 364}"
22,1,272,0,0.3977143,"\int \frac{(e x)^m \left(a+b x^n\right)^3 \left(A+B x^n\right)}{c+d x^n} \, dx","Int[((e*x)^m*(a + b*x^n)^3*(A + B*x^n))/(c + d*x^n),x]","\frac{(e x)^{m+1} \left(-3 a^2 b d^2 (B c-A d)+a^3 B d^3+3 a b^2 c d (B c-A d)+b^3 \left(-c^2\right) (B c-A d)\right)}{d^4 e (m+1)}+\frac{b x^{n+1} (e x)^m \left(3 a^2 B d^2-3 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 (m+n+1)}-\frac{b^2 x^{2 n+1} (e x)^m (-3 a B d-A b d+b B c)}{d^2 (m+2 n+1)}+\frac{(e x)^{m+1} (b c-a d)^3 (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d^4 e (m+1)}+\frac{b^3 B x^{3 n+1} (e x)^m}{d (m+3 n+1)}","\frac{(e x)^{m+1} \left(-3 a^2 b d^2 (B c-A d)+a^3 B d^3+3 a b^2 c d (B c-A d)+b^3 \left(-c^2\right) (B c-A d)\right)}{d^4 e (m+1)}+\frac{b x^{n+1} (e x)^m \left(3 a^2 B d^2-3 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 (m+n+1)}-\frac{b^2 x^{2 n+1} (e x)^m (-3 a B d-A b d+b B c)}{d^2 (m+2 n+1)}+\frac{(e x)^{m+1} (b c-a d)^3 (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d^4 e (m+1)}+\frac{b^3 B x^{3 n+1} (e x)^m}{d (m+3 n+1)}",1,"(b*(3*a^2*B*d^2 + b^2*c*(B*c - A*d) - 3*a*b*d*(B*c - A*d))*x^(1 + n)*(e*x)^m)/(d^3*(1 + m + n)) - (b^2*(b*B*c - A*b*d - 3*a*B*d)*x^(1 + 2*n)*(e*x)^m)/(d^2*(1 + m + 2*n)) + (b^3*B*x^(1 + 3*n)*(e*x)^m)/(d*(1 + m + 3*n)) + ((a^3*B*d^3 - b^3*c^2*(B*c - A*d) + 3*a*b^2*c*d*(B*c - A*d) - 3*a^2*b*d^2*(B*c - A*d))*(e*x)^(1 + m))/(d^4*e*(1 + m)) + ((b*c - a*d)^3*(B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*d^4*e*(1 + m))","A",9,4,31,0.1290,1,"{570, 20, 30, 364}"
23,1,187,0,0.2540683,"\int \frac{(e x)^m \left(a+b x^n\right)^2 \left(A+B x^n\right)}{c+d x^n} \, dx","Int[((e*x)^m*(a + b*x^n)^2*(A + B*x^n))/(c + d*x^n),x]","\frac{(e x)^{m+1} \left(a^2 B d^2-2 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 e (m+1)}-\frac{(e x)^{m+1} (b c-a d)^2 (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d^3 e (m+1)}-\frac{b x^{n+1} (e x)^m (-2 a B d-A b d+b B c)}{d^2 (m+n+1)}+\frac{b^2 B x^{2 n+1} (e x)^m}{d (m+2 n+1)}","\frac{(e x)^{m+1} \left(a^2 B d^2-2 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 e (m+1)}-\frac{(e x)^{m+1} (b c-a d)^2 (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d^3 e (m+1)}-\frac{b x^{n+1} (e x)^m (-2 a B d-A b d+b B c)}{d^2 (m+n+1)}+\frac{b^2 B x^{2 n+1} (e x)^m}{d (m+2 n+1)}",1,"-((b*(b*B*c - A*b*d - 2*a*B*d)*x^(1 + n)*(e*x)^m)/(d^2*(1 + m + n))) + (b^2*B*x^(1 + 2*n)*(e*x)^m)/(d*(1 + m + 2*n)) + ((a^2*B*d^2 + b^2*c*(B*c - A*d) - 2*a*b*d*(B*c - A*d))*(e*x)^(1 + m))/(d^3*e*(1 + m)) - ((b*c - a*d)^2*(B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*d^3*e*(1 + m))","A",7,4,31,0.1290,1,"{570, 20, 30, 364}"
24,1,122,0,0.1261767,"\int \frac{(e x)^m \left(a+b x^n\right) \left(A+B x^n\right)}{c+d x^n} \, dx","Int[((e*x)^m*(a + b*x^n)*(A + B*x^n))/(c + d*x^n),x]","\frac{(e x)^{m+1} (b c-a d) (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d^2 e (m+1)}-\frac{(e x)^{m+1} (-a B d-A b d+b B c)}{d^2 e (m+1)}+\frac{b B x^{n+1} (e x)^m}{d (m+n+1)}","\frac{(e x)^{m+1} (b c-a d) (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d^2 e (m+1)}-\frac{(e x)^{m+1} (-a B d-A b d+b B c)}{d^2 e (m+1)}+\frac{b B x^{n+1} (e x)^m}{d (m+n+1)}",1,"(b*B*x^(1 + n)*(e*x)^m)/(d*(1 + m + n)) - ((b*B*c - A*b*d - a*B*d)*(e*x)^(1 + m))/(d^2*e*(1 + m)) + ((b*c - a*d)*(B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*d^2*e*(1 + m))","A",5,4,29,0.1379,1,"{570, 20, 30, 364}"
25,1,78,0,0.0395393,"\int \frac{(e x)^m \left(A+B x^n\right)}{c+d x^n} \, dx","Int[((e*x)^m*(A + B*x^n))/(c + d*x^n),x]","\frac{B (e x)^{m+1}}{d e (m+1)}-\frac{(e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d e (m+1)}","\frac{B (e x)^{m+1}}{d e (m+1)}-\frac{(e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c d e (m+1)}",1,"(B*(e*x)^(1 + m))/(d*e*(1 + m)) - ((B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*d*e*(1 + m))","A",2,2,22,0.09091,1,"{459, 364}"
26,1,127,0,0.1440562,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)),x]","\frac{(e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a e (m+1) (b c-a d)}+\frac{(e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)}","\frac{(e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a e (m+1) (b c-a d)}+\frac{(e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)}",1,"((A*b - a*B)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*(b*c - a*d)*e*(1 + m)) + ((B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*(b*c - a*d)*e*(1 + m))","A",4,2,31,0.06452,1,"{597, 364}"
27,1,212,0,0.5288391,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)),x]","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (a d (m-2 n+1)-b c (m-n+1))+a B (b c (m+1)-a d (m-n+1)))}{a^2 e (m+1) n (b c-a d)^2}-\frac{d (e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)^2}+\frac{(e x)^{m+1} (A b-a B)}{a e n (b c-a d) \left(a+b x^n\right)}","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (a d (m-2 n+1)-b c (m-n+1))+a B (b c (m+1)-a d (m-n+1)))}{a^2 e (m+1) n (b c-a d)^2}-\frac{d (e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)^2}+\frac{(e x)^{m+1} (A b-a B)}{a e n (b c-a d) \left(a+b x^n\right)}",1,"((A*b - a*B)*(e*x)^(1 + m))/(a*(b*c - a*d)*e*n*(a + b*x^n)) + ((A*b*(a*d*(1 + m - 2*n) - b*c*(1 + m - n)) + a*B*(b*c*(1 + m) - a*d*(1 + m - n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*(b*c - a*d)^2*e*(1 + m)*n) - (d*(B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*(b*c - a*d)^2*e*(1 + m))","A",5,3,31,0.09677,1,"{595, 597, 364}"
28,1,407,0,1.2471762,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(a+b x^n\right)^3 \left(c+d x^n\right)} \, dx","Int[((e*x)^m*(A + B*x^n))/((a + b*x^n)^3*(c + d*x^n)),x]","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) \left(A b \left(a^2 d^2 \left(m^2+m (2-5 n)+6 n^2-5 n+1\right)-2 a b c d \left(m^2+m (2-4 n)+3 n^2-4 n+1\right)+b^2 c^2 \left(m^2+m (2-3 n)+2 n^2-3 n+1\right)\right)+a B \left(-a^2 d^2 \left(m^2+m (2-3 n)+2 n^2-3 n+1\right)+2 a b c d (m+1) (m-2 n+1)-b^2 c^2 (m+1) (m-n+1)\right)\right)}{2 a^3 e (m+1) n^2 (b c-a d)^3}+\frac{(e x)^{m+1} (A b (a d (m-4 n+1)-b c (m-2 n+1))+a B (b c (m+1)-a d (m-2 n+1)))}{2 a^2 e n^2 (b c-a d)^2 \left(a+b x^n\right)}+\frac{d^2 (e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)^3}+\frac{(e x)^{m+1} (A b-a B)}{2 a e n (b c-a d) \left(a+b x^n\right)^2}","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) \left(A b \left(a^2 d^2 \left(m^2+m (2-5 n)+6 n^2-5 n+1\right)-2 a b c d \left(m^2+m (2-4 n)+3 n^2-4 n+1\right)+b^2 c^2 \left(m^2+m (2-3 n)+2 n^2-3 n+1\right)\right)+a B \left(-a^2 d^2 \left(m^2+m (2-3 n)+2 n^2-3 n+1\right)+2 a b c d (m+1) (m-2 n+1)-b^2 c^2 (m+1) (m-n+1)\right)\right)}{2 a^3 e (m+1) n^2 (b c-a d)^3}+\frac{(e x)^{m+1} (A b (a d (m-4 n+1)-b c (m-2 n+1))+a B (b c (m+1)-a d (m-2 n+1)))}{2 a^2 e n^2 (b c-a d)^2 \left(a+b x^n\right)}+\frac{d^2 (e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)^3}+\frac{(e x)^{m+1} (A b-a B)}{2 a e n (b c-a d) \left(a+b x^n\right)^2}",1,"((A*b - a*B)*(e*x)^(1 + m))/(2*a*(b*c - a*d)*e*n*(a + b*x^n)^2) + ((A*b*(a*d*(1 + m - 4*n) - b*c*(1 + m - 2*n)) + a*B*(b*c*(1 + m) - a*d*(1 + m - 2*n)))*(e*x)^(1 + m))/(2*a^2*(b*c - a*d)^2*e*n^2*(a + b*x^n)) + ((a*B*(2*a*b*c*d*(1 + m)*(1 + m - 2*n) - b^2*c^2*(1 + m)*(1 + m - n) - a^2*d^2*(1 + m^2 + m*(2 - 3*n) - 3*n + 2*n^2)) + A*b*(b^2*c^2*(1 + m^2 + m*(2 - 3*n) - 3*n + 2*n^2) - 2*a*b*c*d*(1 + m^2 + m*(2 - 4*n) - 4*n + 3*n^2) + a^2*d^2*(1 + m^2 + m*(2 - 5*n) - 5*n + 6*n^2)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(2*a^3*(b*c - a*d)^3*e*(1 + m)*n^2) + (d^2*(B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*(b*c - a*d)^3*e*(1 + m))","A",6,3,31,0.09677,1,"{595, 597, 364}"
29,1,381,0,1.1347243,"\int \frac{(e x)^m \left(a+b x^n\right)^3 \left(A+B x^n\right)}{\left(c+d x^n\right)^2} \, dx","Int[((e*x)^m*(a + b*x^n)^3*(A + B*x^n))/(c + d*x^n)^2,x]","-\frac{b (e x)^{m+1} \left(3 a^2 d^2 (A d (m+1)-B c (m+n+1))-3 a b c d (A d (m+n+1)-B c (m+2 n+1))+b^2 c^2 (A d (m+2 n+1)-B c (m+3 n+1))\right)}{c d^4 e (m+1) n}-\frac{b^2 x^{n+1} (e x)^m (3 a d (A d (m+n+1)-B c (m+2 n+1))-b c (A d (m+2 n+1)-B c (m+3 n+1)))}{c d^3 n (m+n+1)}+\frac{(e x)^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m+2 n+1)-B c (m+3 n+1)))}{c^2 d^4 e (m+1) n}-\frac{(e x)^{m+1} \left(a+b x^n\right)^3 (B c-A d)}{c d e n \left(c+d x^n\right)}-\frac{b^3 x^{2 n+1} (e x)^m \left(A-\frac{B c (m+3 n+1)}{d (m+2 n+1)}\right)}{c d n}","-\frac{b (e x)^{m+1} \left(3 a^2 d^2 (A d (m+1)-B c (m+n+1))-3 a b c d (A d (m+n+1)-B c (m+2 n+1))+b^2 c^2 (A d (m+2 n+1)-B c (m+3 n+1))\right)}{c d^4 e (m+1) n}-\frac{b^2 x^{n+1} (e x)^m (3 a d (A d (m+n+1)-B c (m+2 n+1))-b c (A d (m+2 n+1)-B c (m+3 n+1)))}{c d^3 n (m+n+1)}+\frac{(e x)^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m+2 n+1)-B c (m+3 n+1)))}{c^2 d^4 e (m+1) n}-\frac{(e x)^{m+1} \left(a+b x^n\right)^3 (B c-A d)}{c d e n \left(c+d x^n\right)}-\frac{b^3 x^{2 n+1} (e x)^m (A d (m+2 n+1)-B c (m+3 n+1))}{c d^2 n (m+2 n+1)}",1,"-((b^2*(3*a*d*(A*d*(1 + m + n) - B*c*(1 + m + 2*n)) - b*c*(A*d*(1 + m + 2*n) - B*c*(1 + m + 3*n)))*x^(1 + n)*(e*x)^m)/(c*d^3*n*(1 + m + n))) - (b^3*(A - (B*c*(1 + m + 3*n))/(d*(1 + m + 2*n)))*x^(1 + 2*n)*(e*x)^m)/(c*d*n) - (b*(3*a^2*d^2*(A*d*(1 + m) - B*c*(1 + m + n)) - 3*a*b*c*d*(A*d*(1 + m + n) - B*c*(1 + m + 2*n)) + b^2*c^2*(A*d*(1 + m + 2*n) - B*c*(1 + m + 3*n)))*(e*x)^(1 + m))/(c*d^4*e*(1 + m)*n) - ((B*c - A*d)*(e*x)^(1 + m)*(a + b*x^n)^3)/(c*d*e*n*(c + d*x^n)) + ((b*c - a*d)^2*(a*d*(B*c*(1 + m) - A*d*(1 + m - n)) + b*c*(A*d*(1 + m + 2*n) - B*c*(1 + m + 3*n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*d^4*e*(1 + m)*n)","A",8,5,31,0.1613,1,"{594, 570, 20, 30, 364}"
30,1,267,0,0.6754408,"\int \frac{(e x)^m \left(a+b x^n\right)^2 \left(A+B x^n\right)}{\left(c+d x^n\right)^2} \, dx","Int[((e*x)^m*(a + b*x^n)^2*(A + B*x^n))/(c + d*x^n)^2,x]","-\frac{(e x)^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m+n+1)-B c (m+2 n+1)))}{c^2 d^3 e (m+1) n}-\frac{b (e x)^{m+1} (2 a d (A d (m+1)-B c (m+n+1))-b c (A d (m+n+1)-B c (m+2 n+1)))}{c d^3 e (m+1) n}-\frac{(e x)^{m+1} \left(a+b x^n\right)^2 (B c-A d)}{c d e n \left(c+d x^n\right)}-\frac{b^2 x^{n+1} (e x)^m (A d (m+n+1)-B c (m+2 n+1))}{c d^2 n (m+n+1)}","-\frac{(e x)^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m+n+1)-B c (m+2 n+1)))}{c^2 d^3 e (m+1) n}-\frac{b (e x)^{m+1} (2 a d (A d (m+1)-B c (m+n+1))-b c (A d (m+n+1)-B c (m+2 n+1)))}{c d^3 e (m+1) n}-\frac{(e x)^{m+1} \left(a+b x^n\right)^2 (B c-A d)}{c d e n \left(c+d x^n\right)}-\frac{b^2 x^{n+1} (e x)^m (A d (m+n+1)-B c (m+2 n+1))}{c d^2 n (m+n+1)}",1,"-((b^2*(A*d*(1 + m + n) - B*c*(1 + m + 2*n))*x^(1 + n)*(e*x)^m)/(c*d^2*n*(1 + m + n))) - (b*(2*a*d*(A*d*(1 + m) - B*c*(1 + m + n)) - b*c*(A*d*(1 + m + n) - B*c*(1 + m + 2*n)))*(e*x)^(1 + m))/(c*d^3*e*(1 + m)*n) - ((B*c - A*d)*(e*x)^(1 + m)*(a + b*x^n)^2)/(c*d*e*n*(c + d*x^n)) - ((b*c - a*d)*(a*d*(B*c*(1 + m) - A*d*(1 + m - n)) + b*c*(A*d*(1 + m + n) - B*c*(1 + m + 2*n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*d^3*e*(1 + m)*n)","A",6,5,31,0.1613,1,"{594, 570, 20, 30, 364}"
31,1,178,0,0.2526498,"\int \frac{(e x)^m \left(a+b x^n\right) \left(A+B x^n\right)}{\left(c+d x^n\right)^2} \, dx","Int[((e*x)^m*(a + b*x^n)*(A + B*x^n))/(c + d*x^n)^2,x]","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (A d (b c (m+1)-a d (m-n+1))+B c (a d (m+1)-b c (m+n+1)))}{c^2 d^2 e (m+1) n}-\frac{(e x)^{m+1} (b c-a d) \left(A+B x^n\right)}{c d e n \left(c+d x^n\right)}-\frac{B (e x)^{m+1} (a d (m+1)-b c (m+n+1))}{c d^2 e (m+1) n}","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (A d (b c (m+1)-a d (m-n+1))+B c (a d (m+1)-b c (m+n+1)))}{c^2 d^2 e (m+1) n}-\frac{(e x)^{m+1} (b c-a d) \left(A+B x^n\right)}{c d e n \left(c+d x^n\right)}-\frac{B (e x)^{m+1} (a d (m+1)-b c (m+n+1))}{c d^2 e (m+1) n}",1,"-((B*(a*d*(1 + m) - b*c*(1 + m + n))*(e*x)^(1 + m))/(c*d^2*e*(1 + m)*n)) - ((b*c - a*d)*(e*x)^(1 + m)*(A + B*x^n))/(c*d*e*n*(c + d*x^n)) + ((A*d*(b*c*(1 + m) - a*d*(1 + m - n)) + B*c*(a*d*(1 + m) - b*c*(1 + m + n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*d^2*e*(1 + m)*n)","A",3,3,29,0.1034,1,"{594, 459, 364}"
32,1,107,0,0.0555015,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(c+d x^n\right)^2} \, dx","Int[((e*x)^m*(A + B*x^n))/(c + d*x^n)^2,x]","\frac{(e x)^{m+1} (B c (m+1)-A d (m-n+1)) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c^2 d e (m+1) n}-\frac{(e x)^{m+1} (B c-A d)}{c d e n \left(c+d x^n\right)}","\frac{(e x)^{m+1} (B c (m+1)-A d (m-n+1)) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c^2 d e (m+1) n}-\frac{(e x)^{m+1} (B c-A d)}{c d e n \left(c+d x^n\right)}",1,"-(((B*c - A*d)*(e*x)^(1 + m))/(c*d*e*n*(c + d*x^n))) + ((B*c*(1 + m) - A*d*(1 + m - n))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*d*e*(1 + m)*n)","A",2,2,22,0.09091,1,"{457, 364}"
33,1,211,0,0.5209732,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(a+b x^n\right) \left(c+d x^n\right)^2} \, dx","Int[((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)^2),x]","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m-2 n+1)-B c (m-n+1)))}{c^2 e (m+1) n (b c-a d)^2}+\frac{b (e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a e (m+1) (b c-a d)^2}+\frac{(e x)^{m+1} (B c-A d)}{c e n (b c-a d) \left(c+d x^n\right)}","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m-2 n+1)-B c (m-n+1)))}{c^2 e (m+1) n (b c-a d)^2}+\frac{b (e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a e (m+1) (b c-a d)^2}+\frac{(e x)^{m+1} (B c-A d)}{c e n (b c-a d) \left(c+d x^n\right)}",1,"((B*c - A*d)*(e*x)^(1 + m))/(c*(b*c - a*d)*e*n*(c + d*x^n)) + (b*(A*b - a*B)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*(b*c - a*d)^2*e*(1 + m)) + ((b*c*(A*d*(1 + m - 2*n) - B*c*(1 + m - n)) + a*d*(B*c*(1 + m) - A*d*(1 + m - n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*(b*c - a*d)^2*e*(1 + m)*n)","A",5,3,31,0.09677,1,"{595, 597, 364}"
34,1,315,0,1.096559,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(a+b x^n\right)^2 \left(c+d x^n\right)^2} \, dx","Int[((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)^2),x]","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (a d (m-3 n+1)-b c (m-n+1))+a B (b c (m+1)-a d (m-2 n+1)))}{a^2 e (m+1) n (b c-a d)^3}-\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m-3 n+1)-B c (m-2 n+1)))}{c^2 e (m+1) n (b c-a d)^3}+\frac{d (e x)^{m+1} (a A d-2 a B c+A b c)}{a c e n (b c-a d)^2 \left(c+d x^n\right)}+\frac{(e x)^{m+1} (A b-a B)}{a e n (b c-a d) \left(a+b x^n\right) \left(c+d x^n\right)}","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (a d (m-3 n+1)-b c (m-n+1))+a B (b c (m+1)-a d (m-2 n+1)))}{a^2 e (m+1) n (b c-a d)^3}-\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m-3 n+1)-B c (m-2 n+1)))}{c^2 e (m+1) n (b c-a d)^3}+\frac{d (e x)^{m+1} (a A d-2 a B c+A b c)}{a c e n (b c-a d)^2 \left(c+d x^n\right)}+\frac{(e x)^{m+1} (A b-a B)}{a e n (b c-a d) \left(a+b x^n\right) \left(c+d x^n\right)}",1,"(d*(A*b*c - 2*a*B*c + a*A*d)*(e*x)^(1 + m))/(a*c*(b*c - a*d)^2*e*n*(c + d*x^n)) + ((A*b - a*B)*(e*x)^(1 + m))/(a*(b*c - a*d)*e*n*(a + b*x^n)*(c + d*x^n)) + (b*(a*B*(b*c*(1 + m) - a*d*(1 + m - 2*n)) + A*b*(a*d*(1 + m - 3*n) - b*c*(1 + m - n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*(b*c - a*d)^3*e*(1 + m)*n) - (d*(b*c*(A*d*(1 + m - 3*n) - B*c*(1 + m - 2*n)) + a*d*(B*c*(1 + m) - A*d*(1 + m - n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*(b*c - a*d)^3*e*(1 + m)*n)","A",6,3,31,0.09677,1,"{595, 597, 364}"
35,1,567,0,2.3406088,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(a+b x^n\right)^3 \left(c+d x^n\right)^2} \, dx","Int[((e*x)^m*(A + B*x^n))/((a + b*x^n)^3*(c + d*x^n)^2),x]","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) \left(A b \left(a^2 d^2 \left(m^2+m (2-7 n)+12 n^2-7 n+1\right)-2 a b c d \left(m^2+m (2-5 n)+4 n^2-5 n+1\right)+b^2 c^2 \left(m^2+m (2-3 n)+2 n^2-3 n+1\right)\right)+a B \left(-a^2 d^2 \left(m^2+m (2-5 n)+6 n^2-5 n+1\right)+2 a b c d (m+1) (m-3 n+1)-b^2 c^2 (m+1) (m-n+1)\right)\right)}{2 a^3 e (m+1) n^2 (b c-a d)^4}+\frac{d (e x)^{m+1} \left(A \left(-2 a^2 d^2 n+a b c d (m-6 n+1)-b^2 c^2 (m-2 n+1)\right)+a B c (b c (m+1)-a d (m-6 n+1))\right)}{2 a^2 c e n^2 (b c-a d)^3 \left(c+d x^n\right)}+\frac{(e x)^{m+1} (A b (a d (m-5 n+1)-b c (m-2 n+1))+a B (b c (m+1)-a d (m-3 n+1)))}{2 a^2 e n^2 (b c-a d)^2 \left(a+b x^n\right) \left(c+d x^n\right)}+\frac{d^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m-4 n+1)-B c (m-3 n+1)))}{c^2 e (m+1) n (b c-a d)^4}+\frac{(e x)^{m+1} (A b-a B)}{2 a e n (b c-a d) \left(a+b x^n\right)^2 \left(c+d x^n\right)}","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) \left(A b \left(a^2 d^2 \left(m^2+m (2-7 n)+12 n^2-7 n+1\right)-2 a b c d \left(m^2+m (2-5 n)+4 n^2-5 n+1\right)+b^2 c^2 \left(m^2+m (2-3 n)+2 n^2-3 n+1\right)\right)+a B \left(-a^2 d^2 \left(m^2+m (2-5 n)+6 n^2-5 n+1\right)+2 a b c d (m+1) (m-3 n+1)-b^2 c^2 (m+1) (m-n+1)\right)\right)}{2 a^3 e (m+1) n^2 (b c-a d)^4}+\frac{d (e x)^{m+1} \left(A \left(-2 a^2 d^2 n+a b c d (m-6 n+1)-b^2 c^2 (m-2 n+1)\right)+a B c (b c (m+1)-a d (m-6 n+1))\right)}{2 a^2 c e n^2 (b c-a d)^3 \left(c+d x^n\right)}+\frac{(e x)^{m+1} (A b (a d (m-5 n+1)-b c (m-2 n+1))+a B (b c (m+1)-a d (m-3 n+1)))}{2 a^2 e n^2 (b c-a d)^2 \left(a+b x^n\right) \left(c+d x^n\right)}+\frac{d^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (B c (m+1)-A d (m-n+1))+b c (A d (m-4 n+1)-B c (m-3 n+1)))}{c^2 e (m+1) n (b c-a d)^4}+\frac{(e x)^{m+1} (A b-a B)}{2 a e n (b c-a d) \left(a+b x^n\right)^2 \left(c+d x^n\right)}",1,"(d*(a*B*c*(b*c*(1 + m) - a*d*(1 + m - 6*n)) + A*(a*b*c*d*(1 + m - 6*n) - b^2*c^2*(1 + m - 2*n) - 2*a^2*d^2*n))*(e*x)^(1 + m))/(2*a^2*c*(b*c - a*d)^3*e*n^2*(c + d*x^n)) + ((A*b - a*B)*(e*x)^(1 + m))/(2*a*(b*c - a*d)*e*n*(a + b*x^n)^2*(c + d*x^n)) + ((a*B*(b*c*(1 + m) - a*d*(1 + m - 3*n)) + A*b*(a*d*(1 + m - 5*n) - b*c*(1 + m - 2*n)))*(e*x)^(1 + m))/(2*a^2*(b*c - a*d)^2*e*n^2*(a + b*x^n)*(c + d*x^n)) + (b*(a*B*(2*a*b*c*d*(1 + m)*(1 + m - 3*n) - b^2*c^2*(1 + m)*(1 + m - n) - a^2*d^2*(1 + m^2 + m*(2 - 5*n) - 5*n + 6*n^2)) + A*b*(b^2*c^2*(1 + m^2 + m*(2 - 3*n) - 3*n + 2*n^2) - 2*a*b*c*d*(1 + m^2 + m*(2 - 5*n) - 5*n + 4*n^2) + a^2*d^2*(1 + m^2 + m*(2 - 7*n) - 7*n + 12*n^2)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(2*a^3*(b*c - a*d)^4*e*(1 + m)*n^2) + (d^2*(b*c*(A*d*(1 + m - 4*n) - B*c*(1 + m - 3*n)) + a*d*(B*c*(1 + m) - A*d*(1 + m - n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*(b*c - a*d)^4*e*(1 + m)*n)","A",7,3,31,0.09677,1,"{595, 597, 364}"
36,1,322,0,0.5568174,"\int \frac{(e x)^m \left(a+b x^n\right)^2 \left(A+B x^n\right)}{\left(c+d x^n\right)^3} \, dx","Int[((e*x)^m*(a + b*x^n)^2*(A + B*x^n))/(c + d*x^n)^3,x]","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (b c (m+1)-a d (m-n+1)) (B c (m+1)-A d (m-2 n+1))-b c (a d (m+1)-b c (m+n+1)) (A d (m+1)-B c (m+2 n+1)))}{2 c^3 d^3 e (m+1) n^2}-\frac{(e x)^{m+1} (b c-a d) \left(a (B c (m+1)-A d (m-2 n+1))-b x^n (A d (m+1)-B c (m+2 n+1))\right)}{2 c^2 d^2 e n^2 \left(c+d x^n\right)}+\frac{b (e x)^{m+1} (a d (m+1)-b c (m+n+1)) (A d (m+1)-B c (m+2 n+1))}{2 c^2 d^3 e (m+1) n^2}-\frac{(e x)^{m+1} \left(a+b x^n\right)^2 (B c-A d)}{2 c d e n \left(c+d x^n\right)^2}","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (a d (b c (m+1)-a d (m-n+1)) (B c (m+1)-A d (m-2 n+1))-b c (a d (m+1)-b c (m+n+1)) (A d (m+1)-B c (m+2 n+1)))}{2 c^3 d^3 e (m+1) n^2}-\frac{(e x)^{m+1} (b c-a d) \left(a (B c (m+1)-A d (m-2 n+1))-b x^n (A d (m+1)-B c (m+2 n+1))\right)}{2 c^2 d^2 e n^2 \left(c+d x^n\right)}+\frac{b (e x)^{m+1} (a d (m+1)-b c (m+n+1)) (A d (m+1)-B c (m+2 n+1))}{2 c^2 d^3 e (m+1) n^2}-\frac{(e x)^{m+1} \left(a+b x^n\right)^2 (B c-A d)}{2 c d e n \left(c+d x^n\right)^2}",1,"(b*(a*d*(1 + m) - b*c*(1 + m + n))*(A*d*(1 + m) - B*c*(1 + m + 2*n))*(e*x)^(1 + m))/(2*c^2*d^3*e*(1 + m)*n^2) - ((B*c - A*d)*(e*x)^(1 + m)*(a + b*x^n)^2)/(2*c*d*e*n*(c + d*x^n)^2) - ((b*c - a*d)*(e*x)^(1 + m)*(a*(B*c*(1 + m) - A*d*(1 + m - 2*n)) - b*(A*d*(1 + m) - B*c*(1 + m + 2*n))*x^n))/(2*c^2*d^2*e*n^2*(c + d*x^n)) + ((a*d*(B*c*(1 + m) - A*d*(1 + m - 2*n))*(b*c*(1 + m) - a*d*(1 + m - n)) - b*c*(a*d*(1 + m) - b*c*(1 + m + n))*(A*d*(1 + m) - B*c*(1 + m + 2*n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(2*c^3*d^3*e*(1 + m)*n^2)","A",4,3,31,0.09677,1,"{594, 459, 364}"
37,1,228,0,0.2805922,"\int \frac{(e x)^m \left(a+b x^n\right) \left(A+B x^n\right)}{\left(c+d x^n\right)^3} \, dx","Int[((e*x)^m*(a + b*x^n)*(A + B*x^n))/(c + d*x^n)^3,x]","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (A d (m-n+1) (b c (m+1)-a d (m-2 n+1))+B c (m+1) (a d (m-n+1)-b c (m+n+1)))}{2 c^3 d^2 e (m+1) n^2}-\frac{(e x)^{m+1} (a d (A d (m-2 n+1)-B c (m-n+1))-b c (A d (m+1)-B c (m+n+1)))}{2 c^2 d^2 e n^2 \left(c+d x^n\right)}-\frac{(e x)^{m+1} (b c-a d) \left(A+B x^n\right)}{2 c d e n \left(c+d x^n\right)^2}","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) (A d (m-n+1) (b c (m+1)-a d (m-2 n+1))+B c (m+1) (a d (m-n+1)-b c (m+n+1)))}{2 c^3 d^2 e (m+1) n^2}-\frac{(e x)^{m+1} (a d (A d (m-2 n+1)-B c (m-n+1))-b c (A d (m+1)-B c (m+n+1)))}{2 c^2 d^2 e n^2 \left(c+d x^n\right)}-\frac{(e x)^{m+1} (b c-a d) \left(A+B x^n\right)}{2 c d e n \left(c+d x^n\right)^2}",1,"-((b*c - a*d)*(e*x)^(1 + m)*(A + B*x^n))/(2*c*d*e*n*(c + d*x^n)^2) - ((a*d*(A*d*(1 + m - 2*n) - B*c*(1 + m - n)) - b*c*(A*d*(1 + m) - B*c*(1 + m + n)))*(e*x)^(1 + m))/(2*c^2*d^2*e*n^2*(c + d*x^n)) - ((A*d*(b*c*(1 + m) - a*d*(1 + m - 2*n))*(1 + m - n) + B*c*(1 + m)*(a*d*(1 + m - n) - b*c*(1 + m + n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(2*c^3*d^2*e*(1 + m)*n^2)","A",3,3,29,0.1034,1,"{594, 457, 364}"
38,1,112,0,0.0556258,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(c+d x^n\right)^3} \, dx","Int[((e*x)^m*(A + B*x^n))/(c + d*x^n)^3,x]","\frac{(e x)^{m+1} (B c (m+1)-A d (m-2 n+1)) \, _2F_1\left(2,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{2 c^3 d e (m+1) n}-\frac{(e x)^{m+1} (B c-A d)}{2 c d e n \left(c+d x^n\right)^2}","\frac{(e x)^{m+1} (B c (m+1)-A d (m-2 n+1)) \, _2F_1\left(2,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{2 c^3 d e (m+1) n}-\frac{(e x)^{m+1} (B c-A d)}{2 c d e n \left(c+d x^n\right)^2}",1,"-((B*c - A*d)*(e*x)^(1 + m))/(2*c*d*e*n*(c + d*x^n)^2) + ((B*c*(1 + m) - A*d*(1 + m - 2*n))*(e*x)^(1 + m)*Hypergeometric2F1[2, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(2*c^3*d*e*(1 + m)*n)","A",2,2,22,0.09091,1,"{457, 364}"
39,1,366,0,1.2169043,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(a+b x^n\right) \left(c+d x^n\right)^3} \, dx","Int[((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)^3),x]","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) \left(-a^2 d^2 (m-n+1) (B c (m+1)-A d (m-2 n+1))+2 a b c d \left(B c (m+1) (m-2 n+1)-A d \left(m^2+m (2-4 n)+3 n^2-4 n+1\right)\right)+b^2 c^2 (m-2 n+1) (A d (m-3 n+1)-B c (m-n+1))\right)}{2 c^3 e (m+1) n^2 (b c-a d)^3}+\frac{b^2 (e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a e (m+1) (b c-a d)^3}+\frac{(e x)^{m+1} (a d (B c (m+1)-A d (m-2 n+1))+b c (A d (m-4 n+1)-B c (m-2 n+1)))}{2 c^2 e n^2 (b c-a d)^2 \left(c+d x^n\right)}+\frac{(e x)^{m+1} (B c-A d)}{2 c e n (b c-a d) \left(c+d x^n\right)^2}","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) \left(-a^2 d^2 (m-n+1) (B c (m+1)-A d (m-2 n+1))+2 a b c d \left(B c (m+1) (m-2 n+1)-A d \left(m^2+m (2-4 n)+3 n^2-4 n+1\right)\right)+b^2 c^2 (m-2 n+1) (A d (m-3 n+1)-B c (m-n+1))\right)}{2 c^3 e (m+1) n^2 (b c-a d)^3}+\frac{b^2 (e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a e (m+1) (b c-a d)^3}+\frac{(e x)^{m+1} (a d (B c (m+1)-A d (m-2 n+1))+b c (A d (m-4 n+1)-B c (m-2 n+1)))}{2 c^2 e n^2 (b c-a d)^2 \left(c+d x^n\right)}+\frac{(e x)^{m+1} (B c-A d)}{2 c e n (b c-a d) \left(c+d x^n\right)^2}",1,"((B*c - A*d)*(e*x)^(1 + m))/(2*c*(b*c - a*d)*e*n*(c + d*x^n)^2) + ((b*c*(A*d*(1 + m - 4*n) - B*c*(1 + m - 2*n)) + a*d*(B*c*(1 + m) - A*d*(1 + m - 2*n)))*(e*x)^(1 + m))/(2*c^2*(b*c - a*d)^2*e*n^2*(c + d*x^n)) + (b^2*(A*b - a*B)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*(b*c - a*d)^3*e*(1 + m)) - ((b^2*c^2*(A*d*(1 + m - 3*n) - B*c*(1 + m - n))*(1 + m - 2*n) - a^2*d^2*(B*c*(1 + m) - A*d*(1 + m - 2*n))*(1 + m - n) + 2*a*b*c*d*(B*c*(1 + m)*(1 + m - 2*n) - A*d*(1 + m^2 + m*(2 - 4*n) - 4*n + 3*n^2)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(2*c^3*(b*c - a*d)^3*e*(1 + m)*n^2)","A",6,3,31,0.09677,1,"{595, 597, 364}"
40,1,482,0,2.0706499,"\int \frac{(e x)^m \left(A+B x^n\right)}{\left(a+b x^n\right)^2 \left(c+d x^n\right)^3} \, dx","Int[((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)^3),x]","\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) \left(-a^2 d^2 (m-n+1) (B c (m+1)-A d (m-2 n+1))+2 a b c d \left(B c (m+1) (m-3 n+1)-A d \left(m^2+m (2-5 n)+4 n^2-5 n+1\right)\right)+b^2 c^2 (m-3 n+1) (A d (m-4 n+1)-B c (m-2 n+1))\right)}{2 c^3 e (m+1) n^2 (b c-a d)^4}-\frac{d (e x)^{m+1} \left(a^2 d (B c (m+1)-A d (m-2 n+1))-a b c (m-6 n+1) (B c-A d)-2 A b^2 c^2 n\right)}{2 a c^2 e n^2 (b c-a d)^3 \left(c+d x^n\right)}+\frac{b^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (a d (m-4 n+1)-b c (m-n+1))+a B (b c (m+1)-a d (m-3 n+1)))}{a^2 e (m+1) n (b c-a d)^4}+\frac{d (e x)^{m+1} (a A d-3 a B c+2 A b c)}{2 a c e n (b c-a d)^2 \left(c+d x^n\right)^2}+\frac{(e x)^{m+1} (A b-a B)}{a e n (b c-a d) \left(a+b x^n\right) \left(c+d x^n\right)^2}","\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right) \left(-a^2 d^2 (m-n+1) (B c (m+1)-A d (m-2 n+1))+2 a b c d \left(B c (m+1) (m-3 n+1)-A d \left(m^2+m (2-5 n)+4 n^2-5 n+1\right)\right)+b^2 c^2 (m-3 n+1) (A d (m-4 n+1)-B c (m-2 n+1))\right)}{2 c^3 e (m+1) n^2 (b c-a d)^4}-\frac{d (e x)^{m+1} \left(a^2 d (B c (m+1)-A d (m-2 n+1))-a b c (m-6 n+1) (B c-A d)-2 A b^2 c^2 n\right)}{2 a c^2 e n^2 (b c-a d)^3 \left(c+d x^n\right)}+\frac{b^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (a d (m-4 n+1)-b c (m-n+1))+a B (b c (m+1)-a d (m-3 n+1)))}{a^2 e (m+1) n (b c-a d)^4}+\frac{d (e x)^{m+1} (a A d-3 a B c+2 A b c)}{2 a c e n (b c-a d)^2 \left(c+d x^n\right)^2}+\frac{(e x)^{m+1} (A b-a B)}{a e n (b c-a d) \left(a+b x^n\right) \left(c+d x^n\right)^2}",1,"(d*(2*A*b*c - 3*a*B*c + a*A*d)*(e*x)^(1 + m))/(2*a*c*(b*c - a*d)^2*e*n*(c + d*x^n)^2) + ((A*b - a*B)*(e*x)^(1 + m))/(a*(b*c - a*d)*e*n*(a + b*x^n)*(c + d*x^n)^2) - (d*(a^2*d*(B*c*(1 + m) - A*d*(1 + m - 2*n)) - a*b*c*(B*c - A*d)*(1 + m - 6*n) - 2*A*b^2*c^2*n)*(e*x)^(1 + m))/(2*a*c^2*(b*c - a*d)^3*e*n^2*(c + d*x^n)) + (b^2*(a*B*(b*c*(1 + m) - a*d*(1 + m - 3*n)) + A*b*(a*d*(1 + m - 4*n) - b*c*(1 + m - n)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*(b*c - a*d)^4*e*(1 + m)*n) + (d*(b^2*c^2*(A*d*(1 + m - 4*n) - B*c*(1 + m - 2*n))*(1 + m - 3*n) - a^2*d^2*(B*c*(1 + m) - A*d*(1 + m - 2*n))*(1 + m - n) + 2*a*b*c*d*(B*c*(1 + m)*(1 + m - 3*n) - A*d*(1 + m^2 + m*(2 - 5*n) - 5*n + 4*n^2)))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(2*c^3*(b*c - a*d)^4*e*(1 + m)*n^2)","A",7,3,31,0.09677,1,"{595, 597, 364}"
41,1,211,0,0.245998,"\int (e x)^m \left(a+b x^n\right)^p \left(A+B x^n\right) \left(c+d x^n\right)^q \, dx","Int[(e*x)^m*(a + b*x^n)^p*(A + B*x^n)*(c + d*x^n)^q,x]","\frac{A (e x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} F_1\left(\frac{m+1}{n};-p,-q;\frac{m+n+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{e (m+1)}+\frac{B x^{n+1} (e x)^m \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} F_1\left(\frac{m+n+1}{n};-p,-q;\frac{m+2 n+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{m+n+1}","\frac{A (e x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} F_1\left(\frac{m+1}{n};-p,-q;\frac{m+n+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{e (m+1)}+\frac{B x^{n+1} (e x)^m \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} F_1\left(\frac{m+n+1}{n};-p,-q;\frac{m+2 n+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{m+n+1}",1,"(A*(e*x)^(1 + m)*(a + b*x^n)^p*(c + d*x^n)^q*AppellF1[(1 + m)/n, -p, -q, (1 + m + n)/n, -((b*x^n)/a), -((d*x^n)/c)])/(e*(1 + m)*(1 + (b*x^n)/a)^p*(1 + (d*x^n)/c)^q) + (B*x^(1 + n)*(e*x)^m*(a + b*x^n)^p*(c + d*x^n)^q*AppellF1[(1 + m + n)/n, -p, -q, (1 + m + 2*n)/n, -((b*x^n)/a), -((d*x^n)/c)])/((1 + m + n)*(1 + (b*x^n)/a)^p*(1 + (d*x^n)/c)^q)","A",7,3,31,0.09677,1,"{598, 511, 510}"
42,1,255,0,0.3274282,"\int (e x)^m \left(a+b x^n\right)^p \left(A+B x^n\right) \left(c+d x^n\right) \, dx","Int[(e*x)^m*(a + b*x^n)^p*(A + B*x^n)*(c + d*x^n),x]","\frac{(e x)^{m+1} \left(a+b x^n\right)^{p+1} (-a B d (m+n+1)+A b d n+b B c (m+n (p+2)+1))}{b^2 e (m+n p+n+1) (m+n (p+2)+1)}-\frac{(e x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right) \left(\frac{a (-a B d (m+n+1)+A b d n+b B c (m+n (p+2)+1))}{b (m+n p+n+1)}+a A d-\frac{A b c (m+n (p+2)+1)}{m+1}\right)}{b e (m+n (p+2)+1)}+\frac{d (e x)^{m+1} \left(A+B x^n\right) \left(a+b x^n\right)^{p+1}}{b e (m+n (p+2)+1)}","-\frac{(e x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right) (A b (m+n p+n+1) (a d (m+1)-b c (m+n (p+2)+1))-a (m+1) (a B d (m+n+1)-b (A d n+B c (m+n (p+2)+1))))}{b^2 e (m+1) (m+n p+n+1) (m+n (p+2)+1)}-\frac{(e x)^{m+1} \left(a+b x^n\right)^{p+1} (a B d (m+n+1)-b (A d n+B c (m+n (p+2)+1)))}{b^2 e (m+n p+n+1) (m+n (p+2)+1)}+\frac{d (e x)^{m+1} \left(A+B x^n\right) \left(a+b x^n\right)^{p+1}}{b e (m+n (p+2)+1)}",1,"((A*b*d*n - a*B*d*(1 + m + n) + b*B*c*(1 + m + n*(2 + p)))*(e*x)^(1 + m)*(a + b*x^n)^(1 + p))/(b^2*e*(1 + m + n + n*p)*(1 + m + n*(2 + p))) + (d*(e*x)^(1 + m)*(a + b*x^n)^(1 + p)*(A + B*x^n))/(b*e*(1 + m + n*(2 + p))) - ((a*A*d - (A*b*c*(1 + m + n*(2 + p)))/(1 + m) + (a*(A*b*d*n - a*B*d*(1 + m + n) + b*B*c*(1 + m + n*(2 + p))))/(b*(1 + m + n + n*p)))*(e*x)^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/(b*e*(1 + m + n*(2 + p))*(1 + (b*x^n)/a)^p)","A",4,4,29,0.1379,1,"{596, 459, 365, 364}"
43,1,164,0,0.1794963,"\int \frac{(e x)^m \left(a+b x^n\right)^p \left(A+B x^n\right)}{c+d x^n} \, dx","Int[((e*x)^m*(a + b*x^n)^p*(A + B*x^n))/(c + d*x^n),x]","\frac{B (e x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{d e (m+1)}-\frac{(e x)^{m+1} (B c-A d) \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} F_1\left(\frac{m+1}{n};-p,1;\frac{m+n+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c d e (m+1)}","\frac{B (e x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{d e (m+1)}-\frac{(e x)^{m+1} (B c-A d) \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} F_1\left(\frac{m+1}{n};-p,1;\frac{m+n+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c d e (m+1)}",1,"-(((B*c - A*d)*(e*x)^(1 + m)*(a + b*x^n)^p*AppellF1[(1 + m)/n, -p, 1, (1 + m + n)/n, -((b*x^n)/a), -((d*x^n)/c)])/(c*d*e*(1 + m)*(1 + (b*x^n)/a)^p)) + (B*(e*x)^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/(d*e*(1 + m)*(1 + (b*x^n)/a)^p)","A",6,5,31,0.1613,1,"{597, 365, 364, 511, 510}"
44,1,304,0,0.5364579,"\int \frac{(e x)^m \left(a+b x^n\right)^p \left(A+B x^n\right)}{\left(c+d x^n\right)^2} \, dx","Int[((e*x)^m*(a + b*x^n)^p*(A + B*x^n))/(c + d*x^n)^2,x]","-\frac{(e x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} (a d (B c (m+1)-A d (m-n+1))+b c (A d (m-n (1-p)+1)-B c (m+n p+1))) F_1\left(\frac{m+1}{n};-p,1;\frac{m+n+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c^2 d e (m+1) n (b c-a d)}-\frac{b (e x)^{m+1} (m+n p+1) (B c-A d) \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c d e (m+1) n (b c-a d)}+\frac{(e x)^{m+1} (B c-A d) \left(a+b x^n\right)^{p+1}}{c e n (b c-a d) \left(c+d x^n\right)}","-\frac{(e x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} (a d (B c (m+1)-A d (m-n+1))+b c (A d (m-n (1-p)+1)-B c (m+n p+1))) F_1\left(\frac{m+1}{n};-p,1;\frac{m+n+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{c^2 d e (m+1) n (b c-a d)}-\frac{b (e x)^{m+1} (m+n p+1) (B c-A d) \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c d e (m+1) n (b c-a d)}+\frac{(e x)^{m+1} (B c-A d) \left(a+b x^n\right)^{p+1}}{c e n (b c-a d) \left(c+d x^n\right)}",1,"((B*c - A*d)*(e*x)^(1 + m)*(a + b*x^n)^(1 + p))/(c*(b*c - a*d)*e*n*(c + d*x^n)) - ((a*d*(B*c*(1 + m) - A*d*(1 + m - n)) + b*c*(A*d*(1 + m - n*(1 - p)) - B*c*(1 + m + n*p)))*(e*x)^(1 + m)*(a + b*x^n)^p*AppellF1[(1 + m)/n, -p, 1, (1 + m + n)/n, -((b*x^n)/a), -((d*x^n)/c)])/(c^2*d*(b*c - a*d)*e*(1 + m)*n*(1 + (b*x^n)/a)^p) - (b*(B*c - A*d)*(1 + m + n*p)*(e*x)^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/(c*d*(b*c - a*d)*e*(1 + m)*n*(1 + (b*x^n)/a)^p)","A",7,6,31,0.1935,1,"{595, 597, 365, 364, 511, 510}"
45,1,139,0,0.1145133,"\int \frac{\left(-a+b x^{n/2}\right)^{-1+\frac{1}{n}} \left(a+b x^{n/2}\right)^{-1+\frac{1}{n}} \left(c+d x^n\right)}{x^2} \, dx","Int[((-a + b*x^(n/2))^(-1 + n^(-1))*(a + b*x^(n/2))^(-1 + n^(-1))*(c + d*x^n))/x^2,x]","\frac{\left(\frac{c}{a^2}+\frac{d}{b^2}\right) \left(b x^{n/2}-a\right)^{\frac{1}{n}} \left(a+b x^{n/2}\right)^{\frac{1}{n}}}{x}-\frac{d \left(b x^{n/2}-a\right)^{\frac{1}{n}} \left(a+b x^{n/2}\right)^{\frac{1}{n}} \left(1-\frac{b^2 x^n}{a^2}\right)^{-1/n} \, _2F_1\left(-\frac{1}{n},-\frac{1}{n};-\frac{1-n}{n};\frac{b^2 x^n}{a^2}\right)}{b^2 x}","\frac{\left(\frac{c}{a^2}+\frac{d}{b^2}\right) \left(b x^{n/2}-a\right)^{\frac{1}{n}} \left(a+b x^{n/2}\right)^{\frac{1}{n}}}{x}-\frac{d \left(b x^{n/2}-a\right)^{\frac{1}{n}} \left(a+b x^{n/2}\right)^{\frac{1}{n}} \left(1-\frac{b^2 x^n}{a^2}\right)^{-1/n} \, _2F_1\left(-\frac{1}{n},-\frac{1}{n};-\frac{1-n}{n};\frac{b^2 x^n}{a^2}\right)}{b^2 x}",1,"((c/a^2 + d/b^2)*(-a + b*x^(n/2))^n^(-1)*(a + b*x^(n/2))^n^(-1))/x - (d*(-a + b*x^(n/2))^n^(-1)*(a + b*x^(n/2))^n^(-1)*Hypergeometric2F1[-n^(-1), -n^(-1), -((1 - n)/n), (b^2*x^n)/a^2])/(b^2*x*(1 - (b^2*x^n)/a^2)^n^(-1))","A",4,4,47,0.08511,1,"{519, 452, 365, 364}"
46,1,167,0,0.1177211,"\int \frac{\left(-a+b x^{n/2}\right)^{\frac{1-n}{n}} \left(a+b x^{n/2}\right)^{\frac{1-n}{n}} \left(c+d x^n\right)}{x^2} \, dx","Int[((-a + b*x^(n/2))^((1 - n)/n)*(a + b*x^(n/2))^((1 - n)/n)*(c + d*x^n))/x^2,x]","\frac{a^2 d \left(b x^{n/2}-a\right)^{\frac{1}{n}-1} \left(a+b x^{n/2}\right)^{\frac{1}{n}-1} \left(1-\frac{b^2 x^n}{a^2}\right)^{-\frac{1-n}{n}} \, _2F_1\left(-\frac{1}{n},-\frac{1}{n};-\frac{1-n}{n};\frac{b^2 x^n}{a^2}\right)}{b^2 x}-\frac{\left(\frac{c}{a^2}+\frac{d}{b^2}\right) \left(b x^{n/2}-a\right)^{\frac{1}{n}-1} \left(a+b x^{n/2}\right)^{\frac{1}{n}-1} \left(a^2-b^2 x^n\right)}{x}","\frac{\left(\frac{c}{a^2}+\frac{d}{b^2}\right) \left(b x^{n/2}-a\right)^{\frac{1}{n}} \left(a+b x^{n/2}\right)^{\frac{1}{n}}}{x}-\frac{d \left(b x^{n/2}-a\right)^{\frac{1}{n}} \left(a+b x^{n/2}\right)^{\frac{1}{n}} \left(1-\frac{b^2 x^n}{a^2}\right)^{-1/n} \, _2F_1\left(-\frac{1}{n},-\frac{1}{n};-\frac{1-n}{n};\frac{b^2 x^n}{a^2}\right)}{b^2 x}",1,"-(((c/a^2 + d/b^2)*(-a + b*x^(n/2))^(-1 + n^(-1))*(a + b*x^(n/2))^(-1 + n^(-1))*(a^2 - b^2*x^n))/x) + (a^2*d*(-a + b*x^(n/2))^(-1 + n^(-1))*(a + b*x^(n/2))^(-1 + n^(-1))*Hypergeometric2F1[-n^(-1), -n^(-1), -((1 - n)/n), (b^2*x^n)/a^2])/(b^2*x*(1 - (b^2*x^n)/a^2)^((1 - n)/n))","A",4,4,55,0.07273,1,"{519, 452, 365, 364}"