1,1,464,0,0.935823," ","integrate((e*x)^m*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n),x, algorithm=""maxima"")","\frac{B b^{3} d e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{B b^{3} c e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, B a b^{2} d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{A b^{3} d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, B a b^{2} c e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A b^{3} c e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, B a^{2} b d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, A a b^{2} d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, B a^{2} b c e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A a b^{2} c e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a^{3} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A a^{2} b d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a^{3} c e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{3 \, A a^{2} b c e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{A a^{3} d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a^{3} c}{e {\left(m + 1\right)}}"," ",0,"B*b^3*d*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + B*b^3*c*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*B*a*b^2*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + A*b^3*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*B*a*b^2*c*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*b^3*c*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*B*a^2*b*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*A*a*b^2*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*B*a^2*b*c*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*a*b^2*c*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a^3*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*a^2*b*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a^3*c*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 3*A*a^2*b*c*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + A*a^3*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a^3*c/(e*(m + 1))","B",0
2,1,332,0,0.860829," ","integrate((e*x)^m*(a+b*x^n)^2*(A+B*x^n)*(c+d*x^n),x, algorithm=""maxima"")","\frac{B b^{2} d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{B b^{2} c e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{2 \, B a b d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A b^{2} d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{2 \, B a b c e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{A b^{2} c e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a^{2} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{2 \, A a b d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a^{2} c e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{2 \, A a b c e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{A a^{2} d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a^{2} c}{e {\left(m + 1\right)}}"," ",0,"B*b^2*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + B*b^2*c*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 2*B*a*b*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*b^2*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 2*B*a*b*c*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + A*b^2*c*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a^2*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 2*A*a*b*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a^2*c*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 2*A*a*b*c*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + A*a^2*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a^2*c/(e*(m + 1))","B",0
3,1,200,0,0.696989," ","integrate((e*x)^m*(a+b*x^n)*(A+B*x^n)*(c+d*x^n),x, algorithm=""maxima"")","\frac{B b d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{B b c e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{A b d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a c e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{A b c e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{A a d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a c}{e {\left(m + 1\right)}}"," ",0,"B*b*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + B*b*c*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + A*b*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a*c*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + A*b*c*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + A*a*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a*c/(e*(m + 1))","A",0
4,1,91,0,0.597759," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n),x, algorithm=""maxima"")","\frac{B d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B c e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{A d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A c}{e {\left(m + 1\right)}}"," ",0,"B*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*c*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + A*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*c/(e*(m + 1))","A",0
5,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)/(a+b*x^n),x, algorithm=""maxima"")","{\left({\left(b^{2} c e^{m} - a b d e^{m}\right)} A - {\left(a b c e^{m} - a^{2} d e^{m}\right)} B\right)} \int \frac{x^{m}}{b^{3} x^{n} + a b^{2}}\,{d x} + \frac{B b d e^{m} {\left(m + 1\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} + {\left(A b d e^{m} {\left(m + n + 1\right)} + {\left(b c e^{m} {\left(m + n + 1\right)} - a d e^{m} {\left(m + n + 1\right)}\right)} B\right)} x x^{m}}{{\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} b^{2}}"," ",0,"((b^2*c*e^m - a*b*d*e^m)*A - (a*b*c*e^m - a^2*d*e^m)*B)*integrate(x^m/(b^3*x^n + a*b^2), x) + (B*b*d*e^m*(m + 1)*x*e^(m*log(x) + n*log(x)) + (A*b*d*e^m*(m + n + 1) + (b*c*e^m*(m + n + 1) - a*d*e^m*(m + n + 1))*B)*x*x^m)/((m^2 + m*(n + 2) + n + 1)*b^2)","F",0
6,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)/(a+b*x^n)^2,x, algorithm=""maxima"")","-{\left({\left(b^{2} c e^{m} {\left(m - n + 1\right)} - a b d e^{m} {\left(m + 1\right)}\right)} A + {\left(a^{2} d e^{m} {\left(m + n + 1\right)} - a b c e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{a b^{3} n x^{n} + a^{2} b^{2} n}\,{d x} + \frac{B a b d e^{m} n x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} + {\left({\left(b^{2} c e^{m} {\left(m + 1\right)} - a b d e^{m} {\left(m + 1\right)}\right)} A + {\left(a^{2} d e^{m} {\left(m + n + 1\right)} - a b c e^{m} {\left(m + 1\right)}\right)} B\right)} x x^{m}}{{\left(m n + n\right)} a b^{3} x^{n} + {\left(m n + n\right)} a^{2} b^{2}}"," ",0,"-((b^2*c*e^m*(m - n + 1) - a*b*d*e^m*(m + 1))*A + (a^2*d*e^m*(m + n + 1) - a*b*c*e^m*(m + 1))*B)*integrate(x^m/(a*b^3*n*x^n + a^2*b^2*n), x) + (B*a*b*d*e^m*n*x*e^(m*log(x) + n*log(x)) + ((b^2*c*e^m*(m + 1) - a*b*d*e^m*(m + 1))*A + (a^2*d*e^m*(m + n + 1) - a*b*c*e^m*(m + 1))*B)*x*x^m)/((m*n + n)*a*b^3*x^n + (m*n + n)*a^2*b^2)","F",0
7,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)/(a+b*x^n)^3,x, algorithm=""maxima"")","{\left({\left({\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} b^{2} c e^{m} - {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a b d e^{m}\right)} A - {\left({\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a b c e^{m} - {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a^{2} d e^{m}\right)} B\right)} \int \frac{x^{m}}{2 \, {\left(a^{2} b^{3} n^{2} x^{n} + a^{3} b^{2} n^{2}\right)}}\,{d x} + \frac{{\left({\left(a^{2} b d e^{m} {\left(m - n + 1\right)} - a b^{2} c e^{m} {\left(m - 3 \, n + 1\right)}\right)} A - {\left(a^{3} d e^{m} {\left(m + n + 1\right)} - a^{2} b c e^{m} {\left(m - n + 1\right)}\right)} B\right)} x x^{m} - {\left({\left(b^{3} c e^{m} {\left(m - 2 \, n + 1\right)} - a b^{2} d e^{m} {\left(m + 1\right)}\right)} A + {\left(a^{2} b d e^{m} {\left(m + 2 \, n + 1\right)} - a b^{2} c e^{m} {\left(m + 1\right)}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left(a^{2} b^{4} n^{2} x^{2 \, n} + 2 \, a^{3} b^{3} n^{2} x^{n} + a^{4} b^{2} n^{2}\right)}}"," ",0,"(((m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*b^2*c*e^m - (m^2 - m*(n - 2) - n + 1)*a*b*d*e^m)*A - ((m^2 - m*(n - 2) - n + 1)*a*b*c*e^m - (m^2 + m*(n + 2) + n + 1)*a^2*d*e^m)*B)*integrate(1/2*x^m/(a^2*b^3*n^2*x^n + a^3*b^2*n^2), x) + 1/2*(((a^2*b*d*e^m*(m - n + 1) - a*b^2*c*e^m*(m - 3*n + 1))*A - (a^3*d*e^m*(m + n + 1) - a^2*b*c*e^m*(m - n + 1))*B)*x*x^m - ((b^3*c*e^m*(m - 2*n + 1) - a*b^2*d*e^m*(m + 1))*A + (a^2*b*d*e^m*(m + 2*n + 1) - a*b^2*c*e^m*(m + 1))*B)*x*e^(m*log(x) + n*log(x)))/(a^2*b^4*n^2*x^(2*n) + 2*a^3*b^3*n^2*x^n + a^4*b^2*n^2)","F",0
8,1,748,0,1.118974," ","integrate((e*x)^m*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n)^2,x, algorithm=""maxima"")","\frac{B b^{3} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 6 \, n \log\left(x\right)\right)}}{m + 6 \, n + 1} + \frac{2 \, B b^{3} c d e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{3 \, B a b^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{A b^{3} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{B b^{3} c^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{6 \, B a b^{2} c d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{2 \, A b^{3} c d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, B a^{2} b d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, A a b^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, B a b^{2} c^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A b^{3} c^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{6 \, B a^{2} b c d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{6 \, A a b^{2} c d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{B a^{3} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, A a^{2} b d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, B a^{2} b c^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A a b^{2} c^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{2 \, B a^{3} c d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{6 \, A a^{2} b c d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{A a^{3} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a^{3} c^{2} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{3 \, A a^{2} b c^{2} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{2 \, A a^{3} c d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a^{3} c^{2}}{e {\left(m + 1\right)}}"," ",0,"B*b^3*d^2*e^m*x*e^(m*log(x) + 6*n*log(x))/(m + 6*n + 1) + 2*B*b^3*c*d*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 3*B*a*b^2*d^2*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + A*b^3*d^2*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + B*b^3*c^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 6*B*a*b^2*c*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 2*A*b^3*c*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*B*a^2*b*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*A*a*b^2*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*B*a*b^2*c^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*b^3*c^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 6*B*a^2*b*c*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 6*A*a*b^2*c*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + B*a^3*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*A*a^2*b*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*B*a^2*b*c^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*a*b^2*c^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 2*B*a^3*c*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 6*A*a^2*b*c*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + A*a^3*d^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a^3*c^2*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 3*A*a^2*b*c^2*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 2*A*a^3*c*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a^3*c^2/(e*(m + 1))","B",0
9,1,540,0,0.905180," ","integrate((e*x)^m*(a+b*x^n)^2*(A+B*x^n)*(c+d*x^n)^2,x, algorithm=""maxima"")","\frac{B b^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{2 \, B b^{2} c d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{2 \, B a b d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{A b^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{B b^{2} c^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{4 \, B a b c d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{2 \, A b^{2} c d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{B a^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{2 \, A a b d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{2 \, B a b c^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{A b^{2} c^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{2 \, B a^{2} c d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{4 \, A a b c d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{A a^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a^{2} c^{2} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{2 \, A a b c^{2} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{2 \, A a^{2} c d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a^{2} c^{2}}{e {\left(m + 1\right)}}"," ",0,"B*b^2*d^2*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 2*B*b^2*c*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 2*B*a*b*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + A*b^2*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + B*b^2*c^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 4*B*a*b*c*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 2*A*b^2*c*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + B*a^2*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 2*A*a*b*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 2*B*a*b*c^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + A*b^2*c^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 2*B*a^2*c*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 4*A*a*b*c*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + A*a^2*d^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a^2*c^2*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 2*A*a*b*c^2*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 2*A*a^2*c*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a^2*c^2/(e*(m + 1))","B",0
10,1,332,0,0.782250," ","integrate((e*x)^m*(a+b*x^n)*(A+B*x^n)*(c+d*x^n)^2,x, algorithm=""maxima"")","\frac{B b d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{2 \, B b c d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{B a d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A b d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{B b c^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{2 \, B a c d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{2 \, A b c d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{A a d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a c^{2} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{A b c^{2} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{2 \, A a c d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a c^{2}}{e {\left(m + 1\right)}}"," ",0,"B*b*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 2*B*b*c*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + B*a*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*b*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + B*b*c^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 2*B*a*c*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 2*A*b*c*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + A*a*d^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a*c^2*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + A*b*c^2*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 2*A*a*c*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a*c^2/(e*(m + 1))","B",0
11,1,155,0,0.634453," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)^2,x, algorithm=""maxima"")","\frac{B d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{2 \, B c d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{A d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B c^{2} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{2 \, A c d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A c^{2}}{e {\left(m + 1\right)}}"," ",0,"B*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 2*B*c*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + A*d^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*c^2*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 2*A*c*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*c^2/(e*(m + 1))","A",0
12,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)^2/(a+b*x^n),x, algorithm=""maxima"")","{\left({\left(b^{3} c^{2} e^{m} - 2 \, a b^{2} c d e^{m} + a^{2} b d^{2} e^{m}\right)} A - {\left(a b^{2} c^{2} e^{m} - 2 \, a^{2} b c d e^{m} + a^{3} d^{2} e^{m}\right)} B\right)} \int \frac{x^{m}}{b^{4} x^{n} + a b^{3}}\,{d x} + \frac{{\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} B b^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left(2 \, {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} b^{2} c d e^{m} - {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a b d^{2} e^{m}\right)} A + {\left({\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} b^{2} c^{2} e^{m} - 2 \, {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a b c d e^{m} + {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a^{2} d^{2} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} A b^{2} d^{2} e^{m} + {\left(2 \, {\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} b^{2} c d e^{m} - {\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} a b d^{2} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} b^{3}}"," ",0,"((b^3*c^2*e^m - 2*a*b^2*c*d*e^m + a^2*b*d^2*e^m)*A - (a*b^2*c^2*e^m - 2*a^2*b*c*d*e^m + a^3*d^2*e^m)*B)*integrate(x^m/(b^4*x^n + a*b^3), x) + ((m^2 + m*(n + 2) + n + 1)*B*b^2*d^2*e^m*x*e^(m*log(x) + 2*n*log(x)) + ((2*(m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*b^2*c*d*e^m - (m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a*b*d^2*e^m)*A + ((m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*b^2*c^2*e^m - 2*(m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a*b*c*d*e^m + (m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a^2*d^2*e^m)*B)*x*x^m + ((m^2 + 2*m*(n + 1) + 2*n + 1)*A*b^2*d^2*e^m + (2*(m^2 + 2*m*(n + 1) + 2*n + 1)*b^2*c*d*e^m - (m^2 + 2*m*(n + 1) + 2*n + 1)*a*b*d^2*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*b^3)","F",0
13,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)^2/(a+b*x^n)^2,x, algorithm=""maxima"")","-{\left({\left(a^{2} b d^{2} e^{m} {\left(m + n + 1\right)} + b^{3} c^{2} e^{m} {\left(m - n + 1\right)} - 2 \, a b^{2} c d e^{m} {\left(m + 1\right)}\right)} A - {\left(a^{3} d^{2} e^{m} {\left(m + 2 \, n + 1\right)} - 2 \, a^{2} b c d e^{m} {\left(m + n + 1\right)} + a b^{2} c^{2} e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{a b^{4} n x^{n} + a^{2} b^{3} n}\,{d x} + \frac{{\left(m n + n\right)} B a b^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left({\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} b^{3} c^{2} e^{m} - 2 \, {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a b^{2} c d e^{m} + {\left(m^{2} + 2 \, m {\left(n + 1\right)} + n^{2} + 2 \, n + 1\right)} a^{2} b d^{2} e^{m}\right)} A - {\left({\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a b^{2} c^{2} e^{m} - 2 \, {\left(m^{2} + 2 \, m {\left(n + 1\right)} + n^{2} + 2 \, n + 1\right)} a^{2} b c d e^{m} + {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a^{3} d^{2} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m n + n^{2} + n\right)} A a b^{2} d^{2} e^{m} + {\left(2 \, {\left(m n + n^{2} + n\right)} a b^{2} c d e^{m} - {\left(m n + 2 \, n^{2} + n\right)} a^{2} b d^{2} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{2} n + {\left(n^{2} + 2 \, n\right)} m + n^{2} + n\right)} a b^{4} x^{n} + {\left(m^{2} n + {\left(n^{2} + 2 \, n\right)} m + n^{2} + n\right)} a^{2} b^{3}}"," ",0,"-((a^2*b*d^2*e^m*(m + n + 1) + b^3*c^2*e^m*(m - n + 1) - 2*a*b^2*c*d*e^m*(m + 1))*A - (a^3*d^2*e^m*(m + 2*n + 1) - 2*a^2*b*c*d*e^m*(m + n + 1) + a*b^2*c^2*e^m*(m + 1))*B)*integrate(x^m/(a*b^4*n*x^n + a^2*b^3*n), x) + ((m*n + n)*B*a*b^2*d^2*e^m*x*e^(m*log(x) + 2*n*log(x)) + (((m^2 + m*(n + 2) + n + 1)*b^3*c^2*e^m - 2*(m^2 + m*(n + 2) + n + 1)*a*b^2*c*d*e^m + (m^2 + 2*m*(n + 1) + n^2 + 2*n + 1)*a^2*b*d^2*e^m)*A - ((m^2 + m*(n + 2) + n + 1)*a*b^2*c^2*e^m - 2*(m^2 + 2*m*(n + 1) + n^2 + 2*n + 1)*a^2*b*c*d*e^m + (m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a^3*d^2*e^m)*B)*x*x^m + ((m*n + n^2 + n)*A*a*b^2*d^2*e^m + (2*(m*n + n^2 + n)*a*b^2*c*d*e^m - (m*n + 2*n^2 + n)*a^2*b*d^2*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^2*n + (n^2 + 2*n)*m + n^2 + n)*a*b^4*x^n + (m^2*n + (n^2 + 2*n)*m + n^2 + n)*a^2*b^3)","F",0
14,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)^2/(a+b*x^n)^3,x, algorithm=""maxima"")","{\left({\left({\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} b^{3} c^{2} e^{m} - 2 \, {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a b^{2} c d e^{m} + {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a^{2} b d^{2} e^{m}\right)} A - {\left({\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a b^{2} c^{2} e^{m} - 2 \, {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a^{2} b c d e^{m} + {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a^{3} d^{2} e^{m}\right)} B\right)} \int \frac{x^{m}}{2 \, {\left(a^{2} b^{4} n^{2} x^{n} + a^{3} b^{3} n^{2}\right)}}\,{d x} + \frac{2 \, B a^{2} b^{2} d^{2} e^{m} n^{2} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} - {\left({\left({\left(m^{2} - m {\left(3 \, n - 2\right)} - 3 \, n + 1\right)} a b^{3} c^{2} e^{m} - 2 \, {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a^{2} b^{2} c d e^{m} + {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a^{3} b d^{2} e^{m}\right)} A - {\left({\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a^{2} b^{2} c^{2} e^{m} - 2 \, {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a^{3} b c d e^{m} + {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a^{4} d^{2} e^{m}\right)} B\right)} x x^{m} - {\left({\left({\left(m^{2} - 2 \, m {\left(n - 1\right)} - 2 \, n + 1\right)} b^{4} c^{2} e^{m} - 2 \, {\left(m^{2} + 2 \, m + 1\right)} a b^{3} c d e^{m} + {\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} a^{2} b^{2} d^{2} e^{m}\right)} A - {\left({\left(m^{2} + 2 \, m + 1\right)} a b^{3} c^{2} e^{m} - 2 \, {\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} a^{2} b^{2} c d e^{m} + {\left(m^{2} + 2 \, m {\left(2 \, n + 1\right)} + 4 \, n^{2} + 4 \, n + 1\right)} a^{3} b d^{2} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left({\left(m n^{2} + n^{2}\right)} a^{2} b^{5} x^{2 \, n} + 2 \, {\left(m n^{2} + n^{2}\right)} a^{3} b^{4} x^{n} + {\left(m n^{2} + n^{2}\right)} a^{4} b^{3}\right)}}"," ",0,"(((m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*b^3*c^2*e^m - 2*(m^2 - m*(n - 2) - n + 1)*a*b^2*c*d*e^m + (m^2 + m*(n + 2) + n + 1)*a^2*b*d^2*e^m)*A - ((m^2 - m*(n - 2) - n + 1)*a*b^2*c^2*e^m - 2*(m^2 + m*(n + 2) + n + 1)*a^2*b*c*d*e^m + (m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a^3*d^2*e^m)*B)*integrate(1/2*x^m/(a^2*b^4*n^2*x^n + a^3*b^3*n^2), x) + 1/2*(2*B*a^2*b^2*d^2*e^m*n^2*x*e^(m*log(x) + 2*n*log(x)) - (((m^2 - m*(3*n - 2) - 3*n + 1)*a*b^3*c^2*e^m - 2*(m^2 - m*(n - 2) - n + 1)*a^2*b^2*c*d*e^m + (m^2 + m*(n + 2) + n + 1)*a^3*b*d^2*e^m)*A - ((m^2 - m*(n - 2) - n + 1)*a^2*b^2*c^2*e^m - 2*(m^2 + m*(n + 2) + n + 1)*a^3*b*c*d*e^m + (m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a^4*d^2*e^m)*B)*x*x^m - (((m^2 - 2*m*(n - 1) - 2*n + 1)*b^4*c^2*e^m - 2*(m^2 + 2*m + 1)*a*b^3*c*d*e^m + (m^2 + 2*m*(n + 1) + 2*n + 1)*a^2*b^2*d^2*e^m)*A - ((m^2 + 2*m + 1)*a*b^3*c^2*e^m - 2*(m^2 + 2*m*(n + 1) + 2*n + 1)*a^2*b^2*c*d*e^m + (m^2 + 2*m*(2*n + 1) + 4*n^2 + 4*n + 1)*a^3*b*d^2*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m*n^2 + n^2)*a^2*b^5*x^(2*n) + 2*(m*n^2 + n^2)*a^3*b^4*x^n + (m*n^2 + n^2)*a^4*b^3)","F",0
15,1,1032,0,1.466561," ","integrate((e*x)^m*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n)^3,x, algorithm=""maxima"")","\frac{B b^{3} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 7 \, n \log\left(x\right)\right)}}{m + 7 \, n + 1} + \frac{3 \, B b^{3} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 6 \, n \log\left(x\right)\right)}}{m + 6 \, n + 1} + \frac{3 \, B a b^{2} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 6 \, n \log\left(x\right)\right)}}{m + 6 \, n + 1} + \frac{A b^{3} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 6 \, n \log\left(x\right)\right)}}{m + 6 \, n + 1} + \frac{3 \, B b^{3} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{9 \, B a b^{2} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{3 \, A b^{3} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{3 \, B a^{2} b d^{3} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{3 \, A a b^{2} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{B b^{3} c^{3} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{9 \, B a b^{2} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, A b^{3} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{9 \, B a^{2} b c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{9 \, A a b^{2} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{B a^{3} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, A a^{2} b d^{3} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, B a b^{2} c^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A b^{3} c^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{9 \, B a^{2} b c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{9 \, A a b^{2} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, B a^{3} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{9 \, A a^{2} b c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A a^{3} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, B a^{2} b c^{3} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A a b^{2} c^{3} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, B a^{3} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{9 \, A a^{2} b c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A a^{3} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a^{3} c^{3} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{3 \, A a^{2} b c^{3} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{3 \, A a^{3} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a^{3} c^{3}}{e {\left(m + 1\right)}}"," ",0,"B*b^3*d^3*e^m*x*e^(m*log(x) + 7*n*log(x))/(m + 7*n + 1) + 3*B*b^3*c*d^2*e^m*x*e^(m*log(x) + 6*n*log(x))/(m + 6*n + 1) + 3*B*a*b^2*d^3*e^m*x*e^(m*log(x) + 6*n*log(x))/(m + 6*n + 1) + A*b^3*d^3*e^m*x*e^(m*log(x) + 6*n*log(x))/(m + 6*n + 1) + 3*B*b^3*c^2*d*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 9*B*a*b^2*c*d^2*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 3*A*b^3*c*d^2*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 3*B*a^2*b*d^3*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 3*A*a*b^2*d^3*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + B*b^3*c^3*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 9*B*a*b^2*c^2*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*A*b^3*c^2*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 9*B*a^2*b*c*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 9*A*a*b^2*c*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + B*a^3*d^3*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*A*a^2*b*d^3*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*B*a*b^2*c^3*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*b^3*c^3*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 9*B*a^2*b*c^2*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 9*A*a*b^2*c^2*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*B*a^3*c*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 9*A*a^2*b*c*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*a^3*d^3*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*B*a^2*b*c^3*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*a*b^2*c^3*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*B*a^3*c^2*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 9*A*a^2*b*c^2*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*a^3*c*d^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a^3*c^3*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 3*A*a^2*b*c^3*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 3*A*a^3*c^2*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a^3*c^3/(e*(m + 1))","B",0
16,1,748,0,0.922896," ","integrate((e*x)^m*(a+b*x^n)^2*(A+B*x^n)*(c+d*x^n)^3,x, algorithm=""maxima"")","\frac{B b^{2} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 6 \, n \log\left(x\right)\right)}}{m + 6 \, n + 1} + \frac{3 \, B b^{2} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{2 \, B a b d^{3} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{A b^{2} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{3 \, B b^{2} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{6 \, B a b c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, A b^{2} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{B a^{2} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{2 \, A a b d^{3} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{B b^{2} c^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{6 \, B a b c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, A b^{2} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, B a^{2} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{6 \, A a b c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A a^{2} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{2 \, B a b c^{3} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{A b^{2} c^{3} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, B a^{2} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{6 \, A a b c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A a^{2} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a^{2} c^{3} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{2 \, A a b c^{3} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{3 \, A a^{2} c^{2} d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a^{2} c^{3}}{e {\left(m + 1\right)}}"," ",0,"B*b^2*d^3*e^m*x*e^(m*log(x) + 6*n*log(x))/(m + 6*n + 1) + 3*B*b^2*c*d^2*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 2*B*a*b*d^3*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + A*b^2*d^3*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 3*B*b^2*c^2*d*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 6*B*a*b*c*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*A*b^2*c*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + B*a^2*d^3*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 2*A*a*b*d^3*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + B*b^2*c^3*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 6*B*a*b*c^2*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*A*b^2*c^2*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*B*a^2*c*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 6*A*a*b*c*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*a^2*d^3*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 2*B*a*b*c^3*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + A*b^2*c^3*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*B*a^2*c^2*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 6*A*a*b*c^2*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*a^2*c*d^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a^2*c^3*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 2*A*a*b*c^3*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 3*A*a^2*c^2*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a^2*c^3/(e*(m + 1))","B",0
17,1,464,0,1.007514," ","integrate((e*x)^m*(a+b*x^n)*(A+B*x^n)*(c+d*x^n)^3,x, algorithm=""maxima"")","\frac{B b d^{3} e^{m} x e^{\left(m \log\left(x\right) + 5 \, n \log\left(x\right)\right)}}{m + 5 \, n + 1} + \frac{3 \, B b c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{B a d^{3} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{A b d^{3} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, B b c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, B a c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, A b c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A a d^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{B b c^{3} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, B a c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A b c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A a c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B a c^{3} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{A b c^{3} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{3 \, A a c^{2} d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A a c^{3}}{e {\left(m + 1\right)}}"," ",0,"B*b*d^3*e^m*x*e^(m*log(x) + 5*n*log(x))/(m + 5*n + 1) + 3*B*b*c*d^2*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + B*a*d^3*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + A*b*d^3*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*B*b*c^2*d*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*B*a*c*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*A*b*c*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*a*d^3*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + B*b*c^3*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*B*a*c^2*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*b*c^2*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*a*c*d^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*a*c^3*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + A*b*c^3*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 3*A*a*c^2*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*a*c^3/(e*(m + 1))","B",0
18,1,219,0,0.844762," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)^3,x, algorithm=""maxima"")","\frac{B d^{3} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)}}{m + 4 \, n + 1} + \frac{3 \, B c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{A d^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)}}{m + 3 \, n + 1} + \frac{3 \, B c^{2} d e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{3 \, A c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)}}{m + 2 \, n + 1} + \frac{B c^{3} e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{3 \, A c^{2} d e^{m} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{m + n + 1} + \frac{\left(e x\right)^{m + 1} A c^{3}}{e {\left(m + 1\right)}}"," ",0,"B*d^3*e^m*x*e^(m*log(x) + 4*n*log(x))/(m + 4*n + 1) + 3*B*c*d^2*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + A*d^3*e^m*x*e^(m*log(x) + 3*n*log(x))/(m + 3*n + 1) + 3*B*c^2*d*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + 3*A*c*d^2*e^m*x*e^(m*log(x) + 2*n*log(x))/(m + 2*n + 1) + B*c^3*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + 3*A*c^2*d*e^m*x*e^(m*log(x) + n*log(x))/(m + n + 1) + (e*x)^(m + 1)*A*c^3/(e*(m + 1))","A",0
19,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)^3/(a+b*x^n),x, algorithm=""maxima"")","{\left({\left(b^{4} c^{3} e^{m} - 3 \, a b^{3} c^{2} d e^{m} + 3 \, a^{2} b^{2} c d^{2} e^{m} - a^{3} b d^{3} e^{m}\right)} A - {\left(a b^{3} c^{3} e^{m} - 3 \, a^{2} b^{2} c^{2} d e^{m} + 3 \, a^{3} b c d^{2} e^{m} - a^{4} d^{3} e^{m}\right)} B\right)} \int \frac{x^{m}}{b^{5} x^{n} + a b^{4}}\,{d x} + \frac{{\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} B b^{3} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)} + {\left({\left(3 \, {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} b^{3} c^{2} d e^{m} - 3 \, {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a b^{2} c d^{2} e^{m} + {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a^{2} b d^{3} e^{m}\right)} A + {\left({\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} b^{3} c^{3} e^{m} - 3 \, {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a b^{2} c^{2} d e^{m} + 3 \, {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a^{2} b c d^{2} e^{m} - {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a^{3} d^{3} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + {\left(3 \, n^{2} + 8 \, n + 3\right)} m + 3 \, n^{2} + 4 \, n + 1\right)} A b^{3} d^{3} e^{m} + {\left(3 \, {\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + {\left(3 \, n^{2} + 8 \, n + 3\right)} m + 3 \, n^{2} + 4 \, n + 1\right)} b^{3} c d^{2} e^{m} - {\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + {\left(3 \, n^{2} + 8 \, n + 3\right)} m + 3 \, n^{2} + 4 \, n + 1\right)} a b^{2} d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left(3 \, {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} b^{3} c d^{2} e^{m} - {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} a b^{2} d^{3} e^{m}\right)} A + {\left(3 \, {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} b^{3} c^{2} d e^{m} - 3 \, {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} a b^{2} c d^{2} e^{m} + {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} a^{2} b d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{4} + 2 \, m^{3} {\left(3 \, n + 2\right)} + {\left(11 \, n^{2} + 18 \, n + 6\right)} m^{2} + 6 \, n^{3} + 2 \, {\left(3 \, n^{3} + 11 \, n^{2} + 9 \, n + 2\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} b^{4}}"," ",0,"((b^4*c^3*e^m - 3*a*b^3*c^2*d*e^m + 3*a^2*b^2*c*d^2*e^m - a^3*b*d^3*e^m)*A - (a*b^3*c^3*e^m - 3*a^2*b^2*c^2*d*e^m + 3*a^3*b*c*d^2*e^m - a^4*d^3*e^m)*B)*integrate(x^m/(b^5*x^n + a*b^4), x) + ((m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*B*b^3*d^3*e^m*x*e^(m*log(x) + 3*n*log(x)) + ((3*(m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*b^3*c^2*d*e^m - 3*(m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a*b^2*c*d^2*e^m + (m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a^2*b*d^3*e^m)*A + ((m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*b^3*c^3*e^m - 3*(m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a*b^2*c^2*d*e^m + 3*(m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a^2*b*c*d^2*e^m - (m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a^3*d^3*e^m)*B)*x*x^m + ((m^3 + m^2*(4*n + 3) + (3*n^2 + 8*n + 3)*m + 3*n^2 + 4*n + 1)*A*b^3*d^3*e^m + (3*(m^3 + m^2*(4*n + 3) + (3*n^2 + 8*n + 3)*m + 3*n^2 + 4*n + 1)*b^3*c*d^2*e^m - (m^3 + m^2*(4*n + 3) + (3*n^2 + 8*n + 3)*m + 3*n^2 + 4*n + 1)*a*b^2*d^3*e^m)*B)*x*e^(m*log(x) + 2*n*log(x)) + ((3*(m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*b^3*c*d^2*e^m - (m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*a*b^2*d^3*e^m)*A + (3*(m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*b^3*c^2*d*e^m - 3*(m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*a*b^2*c*d^2*e^m + (m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*a^2*b*d^3*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^4 + 2*m^3*(3*n + 2) + (11*n^2 + 18*n + 6)*m^2 + 6*n^3 + 2*(3*n^3 + 11*n^2 + 9*n + 2)*m + 11*n^2 + 6*n + 1)*b^4)","F",0
20,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)*(c+d*x^n)^3/(a+b*x^n)^2,x, algorithm=""maxima"")","{\left({\left(a^{3} b d^{3} e^{m} {\left(m + 2 \, n + 1\right)} - 3 \, a^{2} b^{2} c d^{2} e^{m} {\left(m + n + 1\right)} - b^{4} c^{3} e^{m} {\left(m - n + 1\right)} + 3 \, a b^{3} c^{2} d e^{m} {\left(m + 1\right)}\right)} A - {\left(a^{4} d^{3} e^{m} {\left(m + 3 \, n + 1\right)} - 3 \, a^{3} b c d^{2} e^{m} {\left(m + 2 \, n + 1\right)} + 3 \, a^{2} b^{2} c^{2} d e^{m} {\left(m + n + 1\right)} - a b^{3} c^{3} e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{a b^{5} n x^{n} + a^{2} b^{4} n}\,{d x} + \frac{{\left(m^{2} n + {\left(n^{2} + 2 \, n\right)} m + n^{2} + n\right)} B a b^{3} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)} + {\left({\left({\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} b^{4} c^{3} e^{m} - 3 \, {\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} a b^{3} c^{2} d e^{m} + 3 \, {\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + 2 \, n^{3} + {\left(5 \, n^{2} + 8 \, n + 3\right)} m + 5 \, n^{2} + 4 \, n + 1\right)} a^{2} b^{2} c d^{2} e^{m} - {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + 4 \, n^{3} + {\left(8 \, n^{2} + 10 \, n + 3\right)} m + 8 \, n^{2} + 5 \, n + 1\right)} a^{3} b d^{3} e^{m}\right)} A - {\left({\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} a b^{3} c^{3} e^{m} - 3 \, {\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + 2 \, n^{3} + {\left(5 \, n^{2} + 8 \, n + 3\right)} m + 5 \, n^{2} + 4 \, n + 1\right)} a^{2} b^{2} c^{2} d e^{m} + 3 \, {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + 4 \, n^{3} + {\left(8 \, n^{2} + 10 \, n + 3\right)} m + 8 \, n^{2} + 5 \, n + 1\right)} a^{3} b c d^{2} e^{m} - {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a^{4} d^{3} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m^{2} n + 2 \, {\left(n^{2} + n\right)} m + 2 \, n^{2} + n\right)} A a b^{3} d^{3} e^{m} + {\left(3 \, {\left(m^{2} n + 2 \, {\left(n^{2} + n\right)} m + 2 \, n^{2} + n\right)} a b^{3} c d^{2} e^{m} - {\left(m^{2} n + {\left(3 \, n^{2} + 2 \, n\right)} m + 3 \, n^{2} + n\right)} a^{2} b^{2} d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left(3 \, {\left(m^{2} n + 2 \, n^{3} + {\left(3 \, n^{2} + 2 \, n\right)} m + 3 \, n^{2} + n\right)} a b^{3} c d^{2} e^{m} - {\left(m^{2} n + 4 \, n^{3} + 2 \, {\left(2 \, n^{2} + n\right)} m + 4 \, n^{2} + n\right)} a^{2} b^{2} d^{3} e^{m}\right)} A + {\left(3 \, {\left(m^{2} n + 2 \, n^{3} + {\left(3 \, n^{2} + 2 \, n\right)} m + 3 \, n^{2} + n\right)} a b^{3} c^{2} d e^{m} - 3 \, {\left(m^{2} n + 4 \, n^{3} + 2 \, {\left(2 \, n^{2} + n\right)} m + 4 \, n^{2} + n\right)} a^{2} b^{2} c d^{2} e^{m} + {\left(m^{2} n + 6 \, n^{3} + {\left(5 \, n^{2} + 2 \, n\right)} m + 5 \, n^{2} + n\right)} a^{3} b d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{3} n + 3 \, {\left(n^{2} + n\right)} m^{2} + 2 \, n^{3} + {\left(2 \, n^{3} + 6 \, n^{2} + 3 \, n\right)} m + 3 \, n^{2} + n\right)} a b^{5} x^{n} + {\left(m^{3} n + 3 \, {\left(n^{2} + n\right)} m^{2} + 2 \, n^{3} + {\left(2 \, n^{3} + 6 \, n^{2} + 3 \, n\right)} m + 3 \, n^{2} + n\right)} a^{2} b^{4}}"," ",0,"((a^3*b*d^3*e^m*(m + 2*n + 1) - 3*a^2*b^2*c*d^2*e^m*(m + n + 1) - b^4*c^3*e^m*(m - n + 1) + 3*a*b^3*c^2*d*e^m*(m + 1))*A - (a^4*d^3*e^m*(m + 3*n + 1) - 3*a^3*b*c*d^2*e^m*(m + 2*n + 1) + 3*a^2*b^2*c^2*d*e^m*(m + n + 1) - a*b^3*c^3*e^m*(m + 1))*B)*integrate(x^m/(a*b^5*n*x^n + a^2*b^4*n), x) + ((m^2*n + (n^2 + 2*n)*m + n^2 + n)*B*a*b^3*d^3*e^m*x*e^(m*log(x) + 3*n*log(x)) + (((m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*b^4*c^3*e^m - 3*(m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*a*b^3*c^2*d*e^m + 3*(m^3 + m^2*(4*n + 3) + 2*n^3 + (5*n^2 + 8*n + 3)*m + 5*n^2 + 4*n + 1)*a^2*b^2*c*d^2*e^m - (m^3 + m^2*(5*n + 3) + 4*n^3 + (8*n^2 + 10*n + 3)*m + 8*n^2 + 5*n + 1)*a^3*b*d^3*e^m)*A - ((m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*a*b^3*c^3*e^m - 3*(m^3 + m^2*(4*n + 3) + 2*n^3 + (5*n^2 + 8*n + 3)*m + 5*n^2 + 4*n + 1)*a^2*b^2*c^2*d*e^m + 3*(m^3 + m^2*(5*n + 3) + 4*n^3 + (8*n^2 + 10*n + 3)*m + 8*n^2 + 5*n + 1)*a^3*b*c*d^2*e^m - (m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a^4*d^3*e^m)*B)*x*x^m + ((m^2*n + 2*(n^2 + n)*m + 2*n^2 + n)*A*a*b^3*d^3*e^m + (3*(m^2*n + 2*(n^2 + n)*m + 2*n^2 + n)*a*b^3*c*d^2*e^m - (m^2*n + (3*n^2 + 2*n)*m + 3*n^2 + n)*a^2*b^2*d^3*e^m)*B)*x*e^(m*log(x) + 2*n*log(x)) + ((3*(m^2*n + 2*n^3 + (3*n^2 + 2*n)*m + 3*n^2 + n)*a*b^3*c*d^2*e^m - (m^2*n + 4*n^3 + 2*(2*n^2 + n)*m + 4*n^2 + n)*a^2*b^2*d^3*e^m)*A + (3*(m^2*n + 2*n^3 + (3*n^2 + 2*n)*m + 3*n^2 + n)*a*b^3*c^2*d*e^m - 3*(m^2*n + 4*n^3 + 2*(2*n^2 + n)*m + 4*n^2 + n)*a^2*b^2*c*d^2*e^m + (m^2*n + 6*n^3 + (5*n^2 + 2*n)*m + 5*n^2 + n)*a^3*b*d^3*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^3*n + 3*(n^2 + n)*m^2 + 2*n^3 + (2*n^3 + 6*n^2 + 3*n)*m + 3*n^2 + n)*a*b^5*x^n + (m^3*n + 3*(n^2 + n)*m^2 + 2*n^3 + (2*n^3 + 6*n^2 + 3*n)*m + 3*n^2 + n)*a^2*b^4)","F",0
21,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^4*(A+B*x^n)/(c+d*x^n),x, algorithm=""maxima"")","{\left({\left(b^{4} c^{4} d e^{m} - 4 \, a b^{3} c^{3} d^{2} e^{m} + 6 \, a^{2} b^{2} c^{2} d^{3} e^{m} - 4 \, a^{3} b c d^{4} e^{m} + a^{4} d^{5} e^{m}\right)} A - {\left(b^{4} c^{5} e^{m} - 4 \, a b^{3} c^{4} d e^{m} + 6 \, a^{2} b^{2} c^{3} d^{2} e^{m} - 4 \, a^{3} b c^{2} d^{3} e^{m} + a^{4} c d^{4} e^{m}\right)} B\right)} \int \frac{x^{m}}{d^{6} x^{n} + c d^{5}}\,{d x} + \frac{{\left(m^{4} + 2 \, m^{3} {\left(3 \, n + 2\right)} + {\left(11 \, n^{2} + 18 \, n + 6\right)} m^{2} + 6 \, n^{3} + 2 \, {\left(3 \, n^{3} + 11 \, n^{2} + 9 \, n + 2\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} B b^{4} d^{4} e^{m} x e^{\left(m \log\left(x\right) + 4 \, n \log\left(x\right)\right)} - {\left({\left({\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} b^{4} c^{3} d e^{m} - 4 \, {\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} a b^{3} c^{2} d^{2} e^{m} + 6 \, {\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} a^{2} b^{2} c d^{3} e^{m} - 4 \, {\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} a^{3} b d^{4} e^{m}\right)} A - {\left({\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} b^{4} c^{4} e^{m} - 4 \, {\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} a b^{3} c^{3} d e^{m} + 6 \, {\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} a^{2} b^{2} c^{2} d^{2} e^{m} - 4 \, {\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} a^{3} b c d^{3} e^{m} + {\left(m^{4} + 2 \, m^{3} {\left(5 \, n + 2\right)} + 24 \, n^{4} + {\left(35 \, n^{2} + 30 \, n + 6\right)} m^{2} + 50 \, n^{3} + 2 \, {\left(25 \, n^{3} + 35 \, n^{2} + 15 \, n + 2\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} a^{4} d^{4} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m^{4} + m^{3} {\left(7 \, n + 4\right)} + {\left(14 \, n^{2} + 21 \, n + 6\right)} m^{2} + 8 \, n^{3} + {\left(8 \, n^{3} + 28 \, n^{2} + 21 \, n + 4\right)} m + 14 \, n^{2} + 7 \, n + 1\right)} A b^{4} d^{4} e^{m} - {\left({\left(m^{4} + m^{3} {\left(7 \, n + 4\right)} + {\left(14 \, n^{2} + 21 \, n + 6\right)} m^{2} + 8 \, n^{3} + {\left(8 \, n^{3} + 28 \, n^{2} + 21 \, n + 4\right)} m + 14 \, n^{2} + 7 \, n + 1\right)} b^{4} c d^{3} e^{m} - 4 \, {\left(m^{4} + m^{3} {\left(7 \, n + 4\right)} + {\left(14 \, n^{2} + 21 \, n + 6\right)} m^{2} + 8 \, n^{3} + {\left(8 \, n^{3} + 28 \, n^{2} + 21 \, n + 4\right)} m + 14 \, n^{2} + 7 \, n + 1\right)} a b^{3} d^{4} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)} - {\left({\left({\left(m^{4} + 4 \, m^{3} {\left(2 \, n + 1\right)} + {\left(19 \, n^{2} + 24 \, n + 6\right)} m^{2} + 12 \, n^{3} + 2 \, {\left(6 \, n^{3} + 19 \, n^{2} + 12 \, n + 2\right)} m + 19 \, n^{2} + 8 \, n + 1\right)} b^{4} c d^{3} e^{m} - 4 \, {\left(m^{4} + 4 \, m^{3} {\left(2 \, n + 1\right)} + {\left(19 \, n^{2} + 24 \, n + 6\right)} m^{2} + 12 \, n^{3} + 2 \, {\left(6 \, n^{3} + 19 \, n^{2} + 12 \, n + 2\right)} m + 19 \, n^{2} + 8 \, n + 1\right)} a b^{3} d^{4} e^{m}\right)} A - {\left({\left(m^{4} + 4 \, m^{3} {\left(2 \, n + 1\right)} + {\left(19 \, n^{2} + 24 \, n + 6\right)} m^{2} + 12 \, n^{3} + 2 \, {\left(6 \, n^{3} + 19 \, n^{2} + 12 \, n + 2\right)} m + 19 \, n^{2} + 8 \, n + 1\right)} b^{4} c^{2} d^{2} e^{m} - 4 \, {\left(m^{4} + 4 \, m^{3} {\left(2 \, n + 1\right)} + {\left(19 \, n^{2} + 24 \, n + 6\right)} m^{2} + 12 \, n^{3} + 2 \, {\left(6 \, n^{3} + 19 \, n^{2} + 12 \, n + 2\right)} m + 19 \, n^{2} + 8 \, n + 1\right)} a b^{3} c d^{3} e^{m} + 6 \, {\left(m^{4} + 4 \, m^{3} {\left(2 \, n + 1\right)} + {\left(19 \, n^{2} + 24 \, n + 6\right)} m^{2} + 12 \, n^{3} + 2 \, {\left(6 \, n^{3} + 19 \, n^{2} + 12 \, n + 2\right)} m + 19 \, n^{2} + 8 \, n + 1\right)} a^{2} b^{2} d^{4} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left({\left(m^{4} + m^{3} {\left(9 \, n + 4\right)} + {\left(26 \, n^{2} + 27 \, n + 6\right)} m^{2} + 24 \, n^{3} + {\left(24 \, n^{3} + 52 \, n^{2} + 27 \, n + 4\right)} m + 26 \, n^{2} + 9 \, n + 1\right)} b^{4} c^{2} d^{2} e^{m} - 4 \, {\left(m^{4} + m^{3} {\left(9 \, n + 4\right)} + {\left(26 \, n^{2} + 27 \, n + 6\right)} m^{2} + 24 \, n^{3} + {\left(24 \, n^{3} + 52 \, n^{2} + 27 \, n + 4\right)} m + 26 \, n^{2} + 9 \, n + 1\right)} a b^{3} c d^{3} e^{m} + 6 \, {\left(m^{4} + m^{3} {\left(9 \, n + 4\right)} + {\left(26 \, n^{2} + 27 \, n + 6\right)} m^{2} + 24 \, n^{3} + {\left(24 \, n^{3} + 52 \, n^{2} + 27 \, n + 4\right)} m + 26 \, n^{2} + 9 \, n + 1\right)} a^{2} b^{2} d^{4} e^{m}\right)} A - {\left({\left(m^{4} + m^{3} {\left(9 \, n + 4\right)} + {\left(26 \, n^{2} + 27 \, n + 6\right)} m^{2} + 24 \, n^{3} + {\left(24 \, n^{3} + 52 \, n^{2} + 27 \, n + 4\right)} m + 26 \, n^{2} + 9 \, n + 1\right)} b^{4} c^{3} d e^{m} - 4 \, {\left(m^{4} + m^{3} {\left(9 \, n + 4\right)} + {\left(26 \, n^{2} + 27 \, n + 6\right)} m^{2} + 24 \, n^{3} + {\left(24 \, n^{3} + 52 \, n^{2} + 27 \, n + 4\right)} m + 26 \, n^{2} + 9 \, n + 1\right)} a b^{3} c^{2} d^{2} e^{m} + 6 \, {\left(m^{4} + m^{3} {\left(9 \, n + 4\right)} + {\left(26 \, n^{2} + 27 \, n + 6\right)} m^{2} + 24 \, n^{3} + {\left(24 \, n^{3} + 52 \, n^{2} + 27 \, n + 4\right)} m + 26 \, n^{2} + 9 \, n + 1\right)} a^{2} b^{2} c d^{3} e^{m} - 4 \, {\left(m^{4} + m^{3} {\left(9 \, n + 4\right)} + {\left(26 \, n^{2} + 27 \, n + 6\right)} m^{2} + 24 \, n^{3} + {\left(24 \, n^{3} + 52 \, n^{2} + 27 \, n + 4\right)} m + 26 \, n^{2} + 9 \, n + 1\right)} a^{3} b d^{4} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{5} + 5 \, m^{4} {\left(2 \, n + 1\right)} + 5 \, {\left(7 \, n^{2} + 8 \, n + 2\right)} m^{3} + 24 \, n^{4} + 5 \, {\left(10 \, n^{3} + 21 \, n^{2} + 12 \, n + 2\right)} m^{2} + 50 \, n^{3} + {\left(24 \, n^{4} + 100 \, n^{3} + 105 \, n^{2} + 40 \, n + 5\right)} m + 35 \, n^{2} + 10 \, n + 1\right)} d^{5}}"," ",0,"((b^4*c^4*d*e^m - 4*a*b^3*c^3*d^2*e^m + 6*a^2*b^2*c^2*d^3*e^m - 4*a^3*b*c*d^4*e^m + a^4*d^5*e^m)*A - (b^4*c^5*e^m - 4*a*b^3*c^4*d*e^m + 6*a^2*b^2*c^3*d^2*e^m - 4*a^3*b*c^2*d^3*e^m + a^4*c*d^4*e^m)*B)*integrate(x^m/(d^6*x^n + c*d^5), x) + ((m^4 + 2*m^3*(3*n + 2) + (11*n^2 + 18*n + 6)*m^2 + 6*n^3 + 2*(3*n^3 + 11*n^2 + 9*n + 2)*m + 11*n^2 + 6*n + 1)*B*b^4*d^4*e^m*x*e^(m*log(x) + 4*n*log(x)) - (((m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*b^4*c^3*d*e^m - 4*(m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*a*b^3*c^2*d^2*e^m + 6*(m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*a^2*b^2*c*d^3*e^m - 4*(m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*a^3*b*d^4*e^m)*A - ((m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*b^4*c^4*e^m - 4*(m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*a*b^3*c^3*d*e^m + 6*(m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*a^2*b^2*c^2*d^2*e^m - 4*(m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*a^3*b*c*d^3*e^m + (m^4 + 2*m^3*(5*n + 2) + 24*n^4 + (35*n^2 + 30*n + 6)*m^2 + 50*n^3 + 2*(25*n^3 + 35*n^2 + 15*n + 2)*m + 35*n^2 + 10*n + 1)*a^4*d^4*e^m)*B)*x*x^m + ((m^4 + m^3*(7*n + 4) + (14*n^2 + 21*n + 6)*m^2 + 8*n^3 + (8*n^3 + 28*n^2 + 21*n + 4)*m + 14*n^2 + 7*n + 1)*A*b^4*d^4*e^m - ((m^4 + m^3*(7*n + 4) + (14*n^2 + 21*n + 6)*m^2 + 8*n^3 + (8*n^3 + 28*n^2 + 21*n + 4)*m + 14*n^2 + 7*n + 1)*b^4*c*d^3*e^m - 4*(m^4 + m^3*(7*n + 4) + (14*n^2 + 21*n + 6)*m^2 + 8*n^3 + (8*n^3 + 28*n^2 + 21*n + 4)*m + 14*n^2 + 7*n + 1)*a*b^3*d^4*e^m)*B)*x*e^(m*log(x) + 3*n*log(x)) - (((m^4 + 4*m^3*(2*n + 1) + (19*n^2 + 24*n + 6)*m^2 + 12*n^3 + 2*(6*n^3 + 19*n^2 + 12*n + 2)*m + 19*n^2 + 8*n + 1)*b^4*c*d^3*e^m - 4*(m^4 + 4*m^3*(2*n + 1) + (19*n^2 + 24*n + 6)*m^2 + 12*n^3 + 2*(6*n^3 + 19*n^2 + 12*n + 2)*m + 19*n^2 + 8*n + 1)*a*b^3*d^4*e^m)*A - ((m^4 + 4*m^3*(2*n + 1) + (19*n^2 + 24*n + 6)*m^2 + 12*n^3 + 2*(6*n^3 + 19*n^2 + 12*n + 2)*m + 19*n^2 + 8*n + 1)*b^4*c^2*d^2*e^m - 4*(m^4 + 4*m^3*(2*n + 1) + (19*n^2 + 24*n + 6)*m^2 + 12*n^3 + 2*(6*n^3 + 19*n^2 + 12*n + 2)*m + 19*n^2 + 8*n + 1)*a*b^3*c*d^3*e^m + 6*(m^4 + 4*m^3*(2*n + 1) + (19*n^2 + 24*n + 6)*m^2 + 12*n^3 + 2*(6*n^3 + 19*n^2 + 12*n + 2)*m + 19*n^2 + 8*n + 1)*a^2*b^2*d^4*e^m)*B)*x*e^(m*log(x) + 2*n*log(x)) + (((m^4 + m^3*(9*n + 4) + (26*n^2 + 27*n + 6)*m^2 + 24*n^3 + (24*n^3 + 52*n^2 + 27*n + 4)*m + 26*n^2 + 9*n + 1)*b^4*c^2*d^2*e^m - 4*(m^4 + m^3*(9*n + 4) + (26*n^2 + 27*n + 6)*m^2 + 24*n^3 + (24*n^3 + 52*n^2 + 27*n + 4)*m + 26*n^2 + 9*n + 1)*a*b^3*c*d^3*e^m + 6*(m^4 + m^3*(9*n + 4) + (26*n^2 + 27*n + 6)*m^2 + 24*n^3 + (24*n^3 + 52*n^2 + 27*n + 4)*m + 26*n^2 + 9*n + 1)*a^2*b^2*d^4*e^m)*A - ((m^4 + m^3*(9*n + 4) + (26*n^2 + 27*n + 6)*m^2 + 24*n^3 + (24*n^3 + 52*n^2 + 27*n + 4)*m + 26*n^2 + 9*n + 1)*b^4*c^3*d*e^m - 4*(m^4 + m^3*(9*n + 4) + (26*n^2 + 27*n + 6)*m^2 + 24*n^3 + (24*n^3 + 52*n^2 + 27*n + 4)*m + 26*n^2 + 9*n + 1)*a*b^3*c^2*d^2*e^m + 6*(m^4 + m^3*(9*n + 4) + (26*n^2 + 27*n + 6)*m^2 + 24*n^3 + (24*n^3 + 52*n^2 + 27*n + 4)*m + 26*n^2 + 9*n + 1)*a^2*b^2*c*d^3*e^m - 4*(m^4 + m^3*(9*n + 4) + (26*n^2 + 27*n + 6)*m^2 + 24*n^3 + (24*n^3 + 52*n^2 + 27*n + 4)*m + 26*n^2 + 9*n + 1)*a^3*b*d^4*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^5 + 5*m^4*(2*n + 1) + 5*(7*n^2 + 8*n + 2)*m^3 + 24*n^4 + 5*(10*n^3 + 21*n^2 + 12*n + 2)*m^2 + 50*n^3 + (24*n^4 + 100*n^3 + 105*n^2 + 40*n + 5)*m + 35*n^2 + 10*n + 1)*d^5)","F",0
22,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^3*(A+B*x^n)/(c+d*x^n),x, algorithm=""maxima"")","-{\left({\left(b^{3} c^{3} d e^{m} - 3 \, a b^{2} c^{2} d^{2} e^{m} + 3 \, a^{2} b c d^{3} e^{m} - a^{3} d^{4} e^{m}\right)} A - {\left(b^{3} c^{4} e^{m} - 3 \, a b^{2} c^{3} d e^{m} + 3 \, a^{2} b c^{2} d^{2} e^{m} - a^{3} c d^{3} e^{m}\right)} B\right)} \int \frac{x^{m}}{d^{5} x^{n} + c d^{4}}\,{d x} + \frac{{\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} B b^{3} d^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)} + {\left({\left({\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} b^{3} c^{2} d e^{m} - 3 \, {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a b^{2} c d^{2} e^{m} + 3 \, {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a^{2} b d^{3} e^{m}\right)} A - {\left({\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} b^{3} c^{3} e^{m} - 3 \, {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a b^{2} c^{2} d e^{m} + 3 \, {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a^{2} b c d^{2} e^{m} - {\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} a^{3} d^{3} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + {\left(3 \, n^{2} + 8 \, n + 3\right)} m + 3 \, n^{2} + 4 \, n + 1\right)} A b^{3} d^{3} e^{m} - {\left({\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + {\left(3 \, n^{2} + 8 \, n + 3\right)} m + 3 \, n^{2} + 4 \, n + 1\right)} b^{3} c d^{2} e^{m} - 3 \, {\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + {\left(3 \, n^{2} + 8 \, n + 3\right)} m + 3 \, n^{2} + 4 \, n + 1\right)} a b^{2} d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} - {\left({\left({\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} b^{3} c d^{2} e^{m} - 3 \, {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} a b^{2} d^{3} e^{m}\right)} A - {\left({\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} b^{3} c^{2} d e^{m} - 3 \, {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} a b^{2} c d^{2} e^{m} + 3 \, {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + {\left(6 \, n^{2} + 10 \, n + 3\right)} m + 6 \, n^{2} + 5 \, n + 1\right)} a^{2} b d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{4} + 2 \, m^{3} {\left(3 \, n + 2\right)} + {\left(11 \, n^{2} + 18 \, n + 6\right)} m^{2} + 6 \, n^{3} + 2 \, {\left(3 \, n^{3} + 11 \, n^{2} + 9 \, n + 2\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} d^{4}}"," ",0,"-((b^3*c^3*d*e^m - 3*a*b^2*c^2*d^2*e^m + 3*a^2*b*c*d^3*e^m - a^3*d^4*e^m)*A - (b^3*c^4*e^m - 3*a*b^2*c^3*d*e^m + 3*a^2*b*c^2*d^2*e^m - a^3*c*d^3*e^m)*B)*integrate(x^m/(d^5*x^n + c*d^4), x) + ((m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*B*b^3*d^3*e^m*x*e^(m*log(x) + 3*n*log(x)) + (((m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*b^3*c^2*d*e^m - 3*(m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a*b^2*c*d^2*e^m + 3*(m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a^2*b*d^3*e^m)*A - ((m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*b^3*c^3*e^m - 3*(m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a*b^2*c^2*d*e^m + 3*(m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a^2*b*c*d^2*e^m - (m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*a^3*d^3*e^m)*B)*x*x^m + ((m^3 + m^2*(4*n + 3) + (3*n^2 + 8*n + 3)*m + 3*n^2 + 4*n + 1)*A*b^3*d^3*e^m - ((m^3 + m^2*(4*n + 3) + (3*n^2 + 8*n + 3)*m + 3*n^2 + 4*n + 1)*b^3*c*d^2*e^m - 3*(m^3 + m^2*(4*n + 3) + (3*n^2 + 8*n + 3)*m + 3*n^2 + 4*n + 1)*a*b^2*d^3*e^m)*B)*x*e^(m*log(x) + 2*n*log(x)) - (((m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*b^3*c*d^2*e^m - 3*(m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*a*b^2*d^3*e^m)*A - ((m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*b^3*c^2*d*e^m - 3*(m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*a*b^2*c*d^2*e^m + 3*(m^3 + m^2*(5*n + 3) + (6*n^2 + 10*n + 3)*m + 6*n^2 + 5*n + 1)*a^2*b*d^3*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^4 + 2*m^3*(3*n + 2) + (11*n^2 + 18*n + 6)*m^2 + 6*n^3 + 2*(3*n^3 + 11*n^2 + 9*n + 2)*m + 11*n^2 + 6*n + 1)*d^4)","F",0
23,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^2*(A+B*x^n)/(c+d*x^n),x, algorithm=""maxima"")","{\left({\left(b^{2} c^{2} d e^{m} - 2 \, a b c d^{2} e^{m} + a^{2} d^{3} e^{m}\right)} A - {\left(b^{2} c^{3} e^{m} - 2 \, a b c^{2} d e^{m} + a^{2} c d^{2} e^{m}\right)} B\right)} \int \frac{x^{m}}{d^{4} x^{n} + c d^{3}}\,{d x} + \frac{{\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} B b^{2} d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} - {\left({\left({\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} b^{2} c d e^{m} - 2 \, {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a b d^{2} e^{m}\right)} A - {\left({\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} b^{2} c^{2} e^{m} - 2 \, {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a b c d e^{m} + {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a^{2} d^{2} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} A b^{2} d^{2} e^{m} - {\left({\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} b^{2} c d e^{m} - 2 \, {\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} a b d^{2} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} d^{3}}"," ",0,"((b^2*c^2*d*e^m - 2*a*b*c*d^2*e^m + a^2*d^3*e^m)*A - (b^2*c^3*e^m - 2*a*b*c^2*d*e^m + a^2*c*d^2*e^m)*B)*integrate(x^m/(d^4*x^n + c*d^3), x) + ((m^2 + m*(n + 2) + n + 1)*B*b^2*d^2*e^m*x*e^(m*log(x) + 2*n*log(x)) - (((m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*b^2*c*d*e^m - 2*(m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a*b*d^2*e^m)*A - ((m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*b^2*c^2*e^m - 2*(m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a*b*c*d*e^m + (m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a^2*d^2*e^m)*B)*x*x^m + ((m^2 + 2*m*(n + 1) + 2*n + 1)*A*b^2*d^2*e^m - ((m^2 + 2*m*(n + 1) + 2*n + 1)*b^2*c*d*e^m - 2*(m^2 + 2*m*(n + 1) + 2*n + 1)*a*b*d^2*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*d^3)","F",0
24,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)*(A+B*x^n)/(c+d*x^n),x, algorithm=""maxima"")","-{\left({\left(b c d e^{m} - a d^{2} e^{m}\right)} A - {\left(b c^{2} e^{m} - a c d e^{m}\right)} B\right)} \int \frac{x^{m}}{d^{3} x^{n} + c d^{2}}\,{d x} + \frac{B b d e^{m} {\left(m + 1\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} + {\left(A b d e^{m} {\left(m + n + 1\right)} - {\left(b c e^{m} {\left(m + n + 1\right)} - a d e^{m} {\left(m + n + 1\right)}\right)} B\right)} x x^{m}}{{\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} d^{2}}"," ",0,"-((b*c*d*e^m - a*d^2*e^m)*A - (b*c^2*e^m - a*c*d*e^m)*B)*integrate(x^m/(d^3*x^n + c*d^2), x) + (B*b*d*e^m*(m + 1)*x*e^(m*log(x) + n*log(x)) + (A*b*d*e^m*(m + n + 1) - (b*c*e^m*(m + n + 1) - a*d*e^m*(m + n + 1))*B)*x*x^m)/((m^2 + m*(n + 2) + n + 1)*d^2)","F",0
25,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(c+d*x^n),x, algorithm=""maxima"")","\frac{B e^{m} x x^{m}}{d {\left(m + 1\right)}} - {\left(B c e^{m} - A d e^{m}\right)} \int \frac{x^{m}}{d^{2} x^{n} + c d}\,{d x}"," ",0,"B*e^m*x*x^m/(d*(m + 1)) - (B*c*e^m - A*d*e^m)*integrate(x^m/(d^2*x^n + c*d), x)","F",0
26,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(a+b*x^n)/(c+d*x^n),x, algorithm=""maxima"")","\int \frac{{\left(B x^{n} + A\right)} \left(e x\right)^{m}}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}}\,{d x}"," ",0,"integrate((B*x^n + A)*(e*x)^m/((b*x^n + a)*(d*x^n + c)), x)","F",0
27,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""maxima"")","-\frac{{\left(B a e^{m} - A b e^{m}\right)} x x^{m}}{a^{2} b c n - a^{3} d n + {\left(a b^{2} c n - a^{2} b d n\right)} x^{n}} - {\left({\left(b^{2} c e^{m} {\left(m - n + 1\right)} - a b d e^{m} {\left(m - 2 \, n + 1\right)}\right)} A + {\left(a^{2} d e^{m} {\left(m - n + 1\right)} - a b c e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{a^{2} b^{2} c^{2} n - 2 \, a^{3} b c d n + a^{4} d^{2} n + {\left(a b^{3} c^{2} n - 2 \, a^{2} b^{2} c d n + a^{3} b d^{2} n\right)} x^{n}}\,{d x} - {\left(B c d e^{m} - A d^{2} e^{m}\right)} \int \frac{x^{m}}{b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{n}}\,{d x}"," ",0,"-(B*a*e^m - A*b*e^m)*x*x^m/(a^2*b*c*n - a^3*d*n + (a*b^2*c*n - a^2*b*d*n)*x^n) - ((b^2*c*e^m*(m - n + 1) - a*b*d*e^m*(m - 2*n + 1))*A + (a^2*d*e^m*(m - n + 1) - a*b*c*e^m*(m + 1))*B)*integrate(x^m/(a^2*b^2*c^2*n - 2*a^3*b*c*d*n + a^4*d^2*n + (a*b^3*c^2*n - 2*a^2*b^2*c*d*n + a^3*b*d^2*n)*x^n), x) - (B*c*d*e^m - A*d^2*e^m)*integrate(x^m/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^n), x)","F",0
28,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(a+b*x^n)^3/(c+d*x^n),x, algorithm=""maxima"")","-{\left({\left({\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} b^{3} c^{2} e^{m} - 2 \, {\left(m^{2} - 2 \, m {\left(2 \, n - 1\right)} + 3 \, n^{2} - 4 \, n + 1\right)} a b^{2} c d e^{m} + {\left(m^{2} - m {\left(5 \, n - 2\right)} + 6 \, n^{2} - 5 \, n + 1\right)} a^{2} b d^{2} e^{m}\right)} A - {\left({\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a b^{2} c^{2} e^{m} - 2 \, {\left(m^{2} - 2 \, m {\left(n - 1\right)} - 2 \, n + 1\right)} a^{2} b c d e^{m} + {\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} a^{3} d^{2} e^{m}\right)} B\right)} \int -\frac{x^{m}}{2 \, {\left(a^{3} b^{3} c^{3} n^{2} - 3 \, a^{4} b^{2} c^{2} d n^{2} + 3 \, a^{5} b c d^{2} n^{2} - a^{6} d^{3} n^{2} + {\left(a^{2} b^{4} c^{3} n^{2} - 3 \, a^{3} b^{3} c^{2} d n^{2} + 3 \, a^{4} b^{2} c d^{2} n^{2} - a^{5} b d^{3} n^{2}\right)} x^{n}\right)}}\,{d x} - {\left(B c d^{2} e^{m} - A d^{3} e^{m}\right)} \int -\frac{x^{m}}{b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3} + {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{n}}\,{d x} - \frac{{\left({\left(a b^{2} c e^{m} {\left(m - 3 \, n + 1\right)} - a^{2} b d e^{m} {\left(m - 5 \, n + 1\right)}\right)} A - {\left(a^{2} b c e^{m} {\left(m - n + 1\right)} - a^{3} d e^{m} {\left(m - 3 \, n + 1\right)}\right)} B\right)} x x^{m} + {\left({\left(b^{3} c e^{m} {\left(m - 2 \, n + 1\right)} - a b^{2} d e^{m} {\left(m - 4 \, n + 1\right)}\right)} A + {\left(a^{2} b d e^{m} {\left(m - 2 \, n + 1\right)} - a b^{2} c e^{m} {\left(m + 1\right)}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left(a^{4} b^{2} c^{2} n^{2} - 2 \, a^{5} b c d n^{2} + a^{6} d^{2} n^{2} + {\left(a^{2} b^{4} c^{2} n^{2} - 2 \, a^{3} b^{3} c d n^{2} + a^{4} b^{2} d^{2} n^{2}\right)} x^{2 \, n} + 2 \, {\left(a^{3} b^{3} c^{2} n^{2} - 2 \, a^{4} b^{2} c d n^{2} + a^{5} b d^{2} n^{2}\right)} x^{n}\right)}}"," ",0,"-(((m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*b^3*c^2*e^m - 2*(m^2 - 2*m*(2*n - 1) + 3*n^2 - 4*n + 1)*a*b^2*c*d*e^m + (m^2 - m*(5*n - 2) + 6*n^2 - 5*n + 1)*a^2*b*d^2*e^m)*A - ((m^2 - m*(n - 2) - n + 1)*a*b^2*c^2*e^m - 2*(m^2 - 2*m*(n - 1) - 2*n + 1)*a^2*b*c*d*e^m + (m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*a^3*d^2*e^m)*B)*integrate(-1/2*x^m/(a^3*b^3*c^3*n^2 - 3*a^4*b^2*c^2*d*n^2 + 3*a^5*b*c*d^2*n^2 - a^6*d^3*n^2 + (a^2*b^4*c^3*n^2 - 3*a^3*b^3*c^2*d*n^2 + 3*a^4*b^2*c*d^2*n^2 - a^5*b*d^3*n^2)*x^n), x) - (B*c*d^2*e^m - A*d^3*e^m)*integrate(-x^m/(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3 + (b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*x^n), x) - 1/2*(((a*b^2*c*e^m*(m - 3*n + 1) - a^2*b*d*e^m*(m - 5*n + 1))*A - (a^2*b*c*e^m*(m - n + 1) - a^3*d*e^m*(m - 3*n + 1))*B)*x*x^m + ((b^3*c*e^m*(m - 2*n + 1) - a*b^2*d*e^m*(m - 4*n + 1))*A + (a^2*b*d*e^m*(m - 2*n + 1) - a*b^2*c*e^m*(m + 1))*B)*x*e^(m*log(x) + n*log(x)))/(a^4*b^2*c^2*n^2 - 2*a^5*b*c*d*n^2 + a^6*d^2*n^2 + (a^2*b^4*c^2*n^2 - 2*a^3*b^3*c*d*n^2 + a^4*b^2*d^2*n^2)*x^(2*n) + 2*(a^3*b^3*c^2*n^2 - 2*a^4*b^2*c*d*n^2 + a^5*b*d^2*n^2)*x^n)","F",0
29,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^3*(A+B*x^n)/(c+d*x^n)^2,x, algorithm=""maxima"")","{\left({\left(b^{3} c^{3} d e^{m} {\left(m + 2 \, n + 1\right)} - 3 \, a b^{2} c^{2} d^{2} e^{m} {\left(m + n + 1\right)} - a^{3} d^{4} e^{m} {\left(m - n + 1\right)} + 3 \, a^{2} b c d^{3} e^{m} {\left(m + 1\right)}\right)} A - {\left(b^{3} c^{4} e^{m} {\left(m + 3 \, n + 1\right)} - 3 \, a b^{2} c^{3} d e^{m} {\left(m + 2 \, n + 1\right)} + 3 \, a^{2} b c^{2} d^{2} e^{m} {\left(m + n + 1\right)} - a^{3} c d^{3} e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{c d^{5} n x^{n} + c^{2} d^{4} n}\,{d x} + \frac{{\left(m^{2} n + {\left(n^{2} + 2 \, n\right)} m + n^{2} + n\right)} B b^{3} c d^{3} e^{m} x e^{\left(m \log\left(x\right) + 3 \, n \log\left(x\right)\right)} - {\left({\left({\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + 4 \, n^{3} + {\left(8 \, n^{2} + 10 \, n + 3\right)} m + 8 \, n^{2} + 5 \, n + 1\right)} b^{3} c^{3} d e^{m} - 3 \, {\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + 2 \, n^{3} + {\left(5 \, n^{2} + 8 \, n + 3\right)} m + 5 \, n^{2} + 4 \, n + 1\right)} a b^{2} c^{2} d^{2} e^{m} + 3 \, {\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} a^{2} b c d^{3} e^{m} - {\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} a^{3} d^{4} e^{m}\right)} A - {\left({\left(m^{3} + 3 \, m^{2} {\left(2 \, n + 1\right)} + 6 \, n^{3} + {\left(11 \, n^{2} + 12 \, n + 3\right)} m + 11 \, n^{2} + 6 \, n + 1\right)} b^{3} c^{4} e^{m} - 3 \, {\left(m^{3} + m^{2} {\left(5 \, n + 3\right)} + 4 \, n^{3} + {\left(8 \, n^{2} + 10 \, n + 3\right)} m + 8 \, n^{2} + 5 \, n + 1\right)} a b^{2} c^{3} d e^{m} + 3 \, {\left(m^{3} + m^{2} {\left(4 \, n + 3\right)} + 2 \, n^{3} + {\left(5 \, n^{2} + 8 \, n + 3\right)} m + 5 \, n^{2} + 4 \, n + 1\right)} a^{2} b c^{2} d^{2} e^{m} - {\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} a^{3} c d^{3} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m^{2} n + 2 \, {\left(n^{2} + n\right)} m + 2 \, n^{2} + n\right)} A b^{3} c d^{3} e^{m} - {\left({\left(m^{2} n + {\left(3 \, n^{2} + 2 \, n\right)} m + 3 \, n^{2} + n\right)} b^{3} c^{2} d^{2} e^{m} - 3 \, {\left(m^{2} n + 2 \, {\left(n^{2} + n\right)} m + 2 \, n^{2} + n\right)} a b^{2} c d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} - {\left({\left({\left(m^{2} n + 4 \, n^{3} + 2 \, {\left(2 \, n^{2} + n\right)} m + 4 \, n^{2} + n\right)} b^{3} c^{2} d^{2} e^{m} - 3 \, {\left(m^{2} n + 2 \, n^{3} + {\left(3 \, n^{2} + 2 \, n\right)} m + 3 \, n^{2} + n\right)} a b^{2} c d^{3} e^{m}\right)} A - {\left({\left(m^{2} n + 6 \, n^{3} + {\left(5 \, n^{2} + 2 \, n\right)} m + 5 \, n^{2} + n\right)} b^{3} c^{3} d e^{m} - 3 \, {\left(m^{2} n + 4 \, n^{3} + 2 \, {\left(2 \, n^{2} + n\right)} m + 4 \, n^{2} + n\right)} a b^{2} c^{2} d^{2} e^{m} + 3 \, {\left(m^{2} n + 2 \, n^{3} + {\left(3 \, n^{2} + 2 \, n\right)} m + 3 \, n^{2} + n\right)} a^{2} b c d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{3} n + 3 \, {\left(n^{2} + n\right)} m^{2} + 2 \, n^{3} + {\left(2 \, n^{3} + 6 \, n^{2} + 3 \, n\right)} m + 3 \, n^{2} + n\right)} c d^{5} x^{n} + {\left(m^{3} n + 3 \, {\left(n^{2} + n\right)} m^{2} + 2 \, n^{3} + {\left(2 \, n^{3} + 6 \, n^{2} + 3 \, n\right)} m + 3 \, n^{2} + n\right)} c^{2} d^{4}}"," ",0,"((b^3*c^3*d*e^m*(m + 2*n + 1) - 3*a*b^2*c^2*d^2*e^m*(m + n + 1) - a^3*d^4*e^m*(m - n + 1) + 3*a^2*b*c*d^3*e^m*(m + 1))*A - (b^3*c^4*e^m*(m + 3*n + 1) - 3*a*b^2*c^3*d*e^m*(m + 2*n + 1) + 3*a^2*b*c^2*d^2*e^m*(m + n + 1) - a^3*c*d^3*e^m*(m + 1))*B)*integrate(x^m/(c*d^5*n*x^n + c^2*d^4*n), x) + ((m^2*n + (n^2 + 2*n)*m + n^2 + n)*B*b^3*c*d^3*e^m*x*e^(m*log(x) + 3*n*log(x)) - (((m^3 + m^2*(5*n + 3) + 4*n^3 + (8*n^2 + 10*n + 3)*m + 8*n^2 + 5*n + 1)*b^3*c^3*d*e^m - 3*(m^3 + m^2*(4*n + 3) + 2*n^3 + (5*n^2 + 8*n + 3)*m + 5*n^2 + 4*n + 1)*a*b^2*c^2*d^2*e^m + 3*(m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*a^2*b*c*d^3*e^m - (m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*a^3*d^4*e^m)*A - ((m^3 + 3*m^2*(2*n + 1) + 6*n^3 + (11*n^2 + 12*n + 3)*m + 11*n^2 + 6*n + 1)*b^3*c^4*e^m - 3*(m^3 + m^2*(5*n + 3) + 4*n^3 + (8*n^2 + 10*n + 3)*m + 8*n^2 + 5*n + 1)*a*b^2*c^3*d*e^m + 3*(m^3 + m^2*(4*n + 3) + 2*n^3 + (5*n^2 + 8*n + 3)*m + 5*n^2 + 4*n + 1)*a^2*b*c^2*d^2*e^m - (m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*a^3*c*d^3*e^m)*B)*x*x^m + ((m^2*n + 2*(n^2 + n)*m + 2*n^2 + n)*A*b^3*c*d^3*e^m - ((m^2*n + (3*n^2 + 2*n)*m + 3*n^2 + n)*b^3*c^2*d^2*e^m - 3*(m^2*n + 2*(n^2 + n)*m + 2*n^2 + n)*a*b^2*c*d^3*e^m)*B)*x*e^(m*log(x) + 2*n*log(x)) - (((m^2*n + 4*n^3 + 2*(2*n^2 + n)*m + 4*n^2 + n)*b^3*c^2*d^2*e^m - 3*(m^2*n + 2*n^3 + (3*n^2 + 2*n)*m + 3*n^2 + n)*a*b^2*c*d^3*e^m)*A - ((m^2*n + 6*n^3 + (5*n^2 + 2*n)*m + 5*n^2 + n)*b^3*c^3*d*e^m - 3*(m^2*n + 4*n^3 + 2*(2*n^2 + n)*m + 4*n^2 + n)*a*b^2*c^2*d^2*e^m + 3*(m^2*n + 2*n^3 + (3*n^2 + 2*n)*m + 3*n^2 + n)*a^2*b*c*d^3*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^3*n + 3*(n^2 + n)*m^2 + 2*n^3 + (2*n^3 + 6*n^2 + 3*n)*m + 3*n^2 + n)*c*d^5*x^n + (m^3*n + 3*(n^2 + n)*m^2 + 2*n^3 + (2*n^3 + 6*n^2 + 3*n)*m + 3*n^2 + n)*c^2*d^4)","F",0
30,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^2*(A+B*x^n)/(c+d*x^n)^2,x, algorithm=""maxima"")","-{\left({\left(b^{2} c^{2} d e^{m} {\left(m + n + 1\right)} + a^{2} d^{3} e^{m} {\left(m - n + 1\right)} - 2 \, a b c d^{2} e^{m} {\left(m + 1\right)}\right)} A - {\left(b^{2} c^{3} e^{m} {\left(m + 2 \, n + 1\right)} - 2 \, a b c^{2} d e^{m} {\left(m + n + 1\right)} + a^{2} c d^{2} e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{c d^{4} n x^{n} + c^{2} d^{3} n}\,{d x} + \frac{{\left(m n + n\right)} B b^{2} c d^{2} e^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left({\left(m^{2} + 2 \, m {\left(n + 1\right)} + n^{2} + 2 \, n + 1\right)} b^{2} c^{2} d e^{m} - 2 \, {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a b c d^{2} e^{m} + {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a^{2} d^{3} e^{m}\right)} A - {\left({\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} b^{2} c^{3} e^{m} - 2 \, {\left(m^{2} + 2 \, m {\left(n + 1\right)} + n^{2} + 2 \, n + 1\right)} a b c^{2} d e^{m} + {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a^{2} c d^{2} e^{m}\right)} B\right)} x x^{m} + {\left({\left(m n + n^{2} + n\right)} A b^{2} c d^{2} e^{m} - {\left({\left(m n + 2 \, n^{2} + n\right)} b^{2} c^{2} d e^{m} - 2 \, {\left(m n + n^{2} + n\right)} a b c d^{2} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{2} n + {\left(n^{2} + 2 \, n\right)} m + n^{2} + n\right)} c d^{4} x^{n} + {\left(m^{2} n + {\left(n^{2} + 2 \, n\right)} m + n^{2} + n\right)} c^{2} d^{3}}"," ",0,"-((b^2*c^2*d*e^m*(m + n + 1) + a^2*d^3*e^m*(m - n + 1) - 2*a*b*c*d^2*e^m*(m + 1))*A - (b^2*c^3*e^m*(m + 2*n + 1) - 2*a*b*c^2*d*e^m*(m + n + 1) + a^2*c*d^2*e^m*(m + 1))*B)*integrate(x^m/(c*d^4*n*x^n + c^2*d^3*n), x) + ((m*n + n)*B*b^2*c*d^2*e^m*x*e^(m*log(x) + 2*n*log(x)) + (((m^2 + 2*m*(n + 1) + n^2 + 2*n + 1)*b^2*c^2*d*e^m - 2*(m^2 + m*(n + 2) + n + 1)*a*b*c*d^2*e^m + (m^2 + m*(n + 2) + n + 1)*a^2*d^3*e^m)*A - ((m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*b^2*c^3*e^m - 2*(m^2 + 2*m*(n + 1) + n^2 + 2*n + 1)*a*b*c^2*d*e^m + (m^2 + m*(n + 2) + n + 1)*a^2*c*d^2*e^m)*B)*x*x^m + ((m*n + n^2 + n)*A*b^2*c*d^2*e^m - ((m*n + 2*n^2 + n)*b^2*c^2*d*e^m - 2*(m*n + n^2 + n)*a*b*c*d^2*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m^2*n + (n^2 + 2*n)*m + n^2 + n)*c*d^4*x^n + (m^2*n + (n^2 + 2*n)*m + n^2 + n)*c^2*d^3)","F",0
31,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)*(A+B*x^n)/(c+d*x^n)^2,x, algorithm=""maxima"")","-{\left({\left(a d^{2} e^{m} {\left(m - n + 1\right)} - b c d e^{m} {\left(m + 1\right)}\right)} A + {\left(b c^{2} e^{m} {\left(m + n + 1\right)} - a c d e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{c d^{3} n x^{n} + c^{2} d^{2} n}\,{d x} + \frac{B b c d e^{m} n x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - {\left({\left(b c d e^{m} {\left(m + 1\right)} - a d^{2} e^{m} {\left(m + 1\right)}\right)} A - {\left(b c^{2} e^{m} {\left(m + n + 1\right)} - a c d e^{m} {\left(m + 1\right)}\right)} B\right)} x x^{m}}{{\left(m n + n\right)} c d^{3} x^{n} + {\left(m n + n\right)} c^{2} d^{2}}"," ",0,"-((a*d^2*e^m*(m - n + 1) - b*c*d*e^m*(m + 1))*A + (b*c^2*e^m*(m + n + 1) - a*c*d*e^m*(m + 1))*B)*integrate(x^m/(c*d^3*n*x^n + c^2*d^2*n), x) + (B*b*c*d*e^m*n*x*e^(m*log(x) + n*log(x)) - ((b*c*d*e^m*(m + 1) - a*d^2*e^m*(m + 1))*A - (b*c^2*e^m*(m + n + 1) - a*c*d*e^m*(m + 1))*B)*x*x^m)/((m*n + n)*c*d^3*x^n + (m*n + n)*c^2*d^2)","F",0
32,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(c+d*x^n)^2,x, algorithm=""maxima"")","-\frac{{\left(B c e^{m} - A d e^{m}\right)} x x^{m}}{c d^{2} n x^{n} + c^{2} d n} - {\left(A d e^{m} {\left(m - n + 1\right)} - B c e^{m} {\left(m + 1\right)}\right)} \int \frac{x^{m}}{c d^{2} n x^{n} + c^{2} d n}\,{d x}"," ",0,"-(B*c*e^m - A*d*e^m)*x*x^m/(c*d^2*n*x^n + c^2*d*n) - (A*d*e^m*(m - n + 1) - B*c*e^m*(m + 1))*integrate(x^m/(c*d^2*n*x^n + c^2*d*n), x)","F",0
33,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(a+b*x^n)/(c+d*x^n)^2,x, algorithm=""maxima"")","\frac{{\left(B c e^{m} - A d e^{m}\right)} x x^{m}}{b c^{3} n - a c^{2} d n + {\left(b c^{2} d n - a c d^{2} n\right)} x^{n}} - {\left({\left(a d^{2} e^{m} {\left(m - n + 1\right)} - b c d e^{m} {\left(m - 2 \, n + 1\right)}\right)} A + {\left(b c^{2} e^{m} {\left(m - n + 1\right)} - a c d e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{b^{2} c^{4} n - 2 \, a b c^{3} d n + a^{2} c^{2} d^{2} n + {\left(b^{2} c^{3} d n - 2 \, a b c^{2} d^{2} n + a^{2} c d^{3} n\right)} x^{n}}\,{d x} - {\left(B a b e^{m} - A b^{2} e^{m}\right)} \int \frac{x^{m}}{a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{n}}\,{d x}"," ",0,"(B*c*e^m - A*d*e^m)*x*x^m/(b*c^3*n - a*c^2*d*n + (b*c^2*d*n - a*c*d^2*n)*x^n) - ((a*d^2*e^m*(m - n + 1) - b*c*d*e^m*(m - 2*n + 1))*A + (b*c^2*e^m*(m - n + 1) - a*c*d*e^m*(m + 1))*B)*integrate(x^m/(b^2*c^4*n - 2*a*b*c^3*d*n + a^2*c^2*d^2*n + (b^2*c^3*d*n - 2*a*b*c^2*d^2*n + a^2*c*d^3*n)*x^n), x) - (B*a*b*e^m - A*b^2*e^m)*integrate(x^m/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^n), x)","F",0
34,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(a+b*x^n)^2/(c+d*x^n)^2,x, algorithm=""maxima"")","{\left({\left(b^{3} c e^{m} {\left(m - n + 1\right)} - a b^{2} d e^{m} {\left(m - 3 \, n + 1\right)}\right)} A + {\left(a^{2} b d e^{m} {\left(m - 2 \, n + 1\right)} - a b^{2} c e^{m} {\left(m + 1\right)}\right)} B\right)} \int -\frac{x^{m}}{a^{2} b^{3} c^{3} n - 3 \, a^{3} b^{2} c^{2} d n + 3 \, a^{4} b c d^{2} n - a^{5} d^{3} n + {\left(a b^{4} c^{3} n - 3 \, a^{2} b^{3} c^{2} d n + 3 \, a^{3} b^{2} c d^{2} n - a^{4} b d^{3} n\right)} x^{n}}\,{d x} - {\left({\left(a d^{3} e^{m} {\left(m - n + 1\right)} - b c d^{2} e^{m} {\left(m - 3 \, n + 1\right)}\right)} A + {\left(b c^{2} d e^{m} {\left(m - 2 \, n + 1\right)} - a c d^{2} e^{m} {\left(m + 1\right)}\right)} B\right)} \int -\frac{x^{m}}{b^{3} c^{5} n - 3 \, a b^{2} c^{4} d n + 3 \, a^{2} b c^{3} d^{2} n - a^{3} c^{2} d^{3} n + {\left(b^{3} c^{4} d n - 3 \, a b^{2} c^{3} d^{2} n + 3 \, a^{2} b c^{2} d^{3} n - a^{3} c d^{4} n\right)} x^{n}}\,{d x} + \frac{{\left({\left(b^{2} c^{2} e^{m} + a^{2} d^{2} e^{m}\right)} A - {\left(a b c^{2} e^{m} + a^{2} c d e^{m}\right)} B\right)} x x^{m} - {\left(2 \, B a b c d e^{m} - {\left(b^{2} c d e^{m} + a b d^{2} e^{m}\right)} A\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{a^{2} b^{2} c^{4} n - 2 \, a^{3} b c^{3} d n + a^{4} c^{2} d^{2} n + {\left(a b^{3} c^{3} d n - 2 \, a^{2} b^{2} c^{2} d^{2} n + a^{3} b c d^{3} n\right)} x^{2 \, n} + {\left(a b^{3} c^{4} n - a^{2} b^{2} c^{3} d n - a^{3} b c^{2} d^{2} n + a^{4} c d^{3} n\right)} x^{n}}"," ",0,"((b^3*c*e^m*(m - n + 1) - a*b^2*d*e^m*(m - 3*n + 1))*A + (a^2*b*d*e^m*(m - 2*n + 1) - a*b^2*c*e^m*(m + 1))*B)*integrate(-x^m/(a^2*b^3*c^3*n - 3*a^3*b^2*c^2*d*n + 3*a^4*b*c*d^2*n - a^5*d^3*n + (a*b^4*c^3*n - 3*a^2*b^3*c^2*d*n + 3*a^3*b^2*c*d^2*n - a^4*b*d^3*n)*x^n), x) - ((a*d^3*e^m*(m - n + 1) - b*c*d^2*e^m*(m - 3*n + 1))*A + (b*c^2*d*e^m*(m - 2*n + 1) - a*c*d^2*e^m*(m + 1))*B)*integrate(-x^m/(b^3*c^5*n - 3*a*b^2*c^4*d*n + 3*a^2*b*c^3*d^2*n - a^3*c^2*d^3*n + (b^3*c^4*d*n - 3*a*b^2*c^3*d^2*n + 3*a^2*b*c^2*d^3*n - a^3*c*d^4*n)*x^n), x) + (((b^2*c^2*e^m + a^2*d^2*e^m)*A - (a*b*c^2*e^m + a^2*c*d*e^m)*B)*x*x^m - (2*B*a*b*c*d*e^m - (b^2*c*d*e^m + a*b*d^2*e^m)*A)*x*e^(m*log(x) + n*log(x)))/(a^2*b^2*c^4*n - 2*a^3*b*c^3*d*n + a^4*c^2*d^2*n + (a*b^3*c^3*d*n - 2*a^2*b^2*c^2*d^2*n + a^3*b*c*d^3*n)*x^(2*n) + (a*b^3*c^4*n - a^2*b^2*c^3*d*n - a^3*b*c^2*d^2*n + a^4*c*d^3*n)*x^n)","F",0
35,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(a+b*x^n)^3/(c+d*x^n)^2,x, algorithm=""maxima"")","{\left({\left({\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} b^{4} c^{2} e^{m} - 2 \, {\left(m^{2} - m {\left(5 \, n - 2\right)} + 4 \, n^{2} - 5 \, n + 1\right)} a b^{3} c d e^{m} + {\left(m^{2} - m {\left(7 \, n - 2\right)} + 12 \, n^{2} - 7 \, n + 1\right)} a^{2} b^{2} d^{2} e^{m}\right)} A - {\left({\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a b^{3} c^{2} e^{m} - 2 \, {\left(m^{2} - m {\left(3 \, n - 2\right)} - 3 \, n + 1\right)} a^{2} b^{2} c d e^{m} + {\left(m^{2} - m {\left(5 \, n - 2\right)} + 6 \, n^{2} - 5 \, n + 1\right)} a^{3} b d^{2} e^{m}\right)} B\right)} \int \frac{x^{m}}{2 \, {\left(a^{3} b^{4} c^{4} n^{2} - 4 \, a^{4} b^{3} c^{3} d n^{2} + 6 \, a^{5} b^{2} c^{2} d^{2} n^{2} - 4 \, a^{6} b c d^{3} n^{2} + a^{7} d^{4} n^{2} + {\left(a^{2} b^{5} c^{4} n^{2} - 4 \, a^{3} b^{4} c^{3} d n^{2} + 6 \, a^{4} b^{3} c^{2} d^{2} n^{2} - 4 \, a^{5} b^{2} c d^{3} n^{2} + a^{6} b d^{4} n^{2}\right)} x^{n}\right)}}\,{d x} - {\left({\left(a d^{4} e^{m} {\left(m - n + 1\right)} - b c d^{3} e^{m} {\left(m - 4 \, n + 1\right)}\right)} A + {\left(b c^{2} d^{2} e^{m} {\left(m - 3 \, n + 1\right)} - a c d^{3} e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{b^{4} c^{6} n - 4 \, a b^{3} c^{5} d n + 6 \, a^{2} b^{2} c^{4} d^{2} n - 4 \, a^{3} b c^{3} d^{3} n + a^{4} c^{2} d^{4} n + {\left(b^{4} c^{5} d n - 4 \, a b^{3} c^{4} d^{2} n + 6 \, a^{2} b^{2} c^{3} d^{3} n - 4 \, a^{3} b c^{2} d^{4} n + a^{4} c d^{5} n\right)} x^{n}}\,{d x} - \frac{{\left({\left(a b^{3} c^{3} e^{m} {\left(m - 3 \, n + 1\right)} - a^{2} b^{2} c^{2} d e^{m} {\left(m - 7 \, n + 1\right)} + 2 \, a^{4} d^{3} e^{m} n\right)} A - {\left(a^{2} b^{2} c^{3} e^{m} {\left(m - n + 1\right)} - a^{3} b c^{2} d e^{m} {\left(m - 5 \, n + 1\right)} + 2 \, a^{4} c d^{2} e^{m} n\right)} B\right)} x x^{m} + {\left({\left(b^{4} c^{2} d e^{m} {\left(m - 2 \, n + 1\right)} - a b^{3} c d^{2} e^{m} {\left(m - 6 \, n + 1\right)} + 2 \, a^{2} b^{2} d^{3} e^{m} n\right)} A + {\left(a^{2} b^{2} c d^{2} e^{m} {\left(m - 6 \, n + 1\right)} - a b^{3} c^{2} d e^{m} {\left(m + 1\right)}\right)} B\right)} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left(b^{4} c^{3} e^{m} {\left(m - 2 \, n + 1\right)} - a^{2} b^{2} c d^{2} e^{m} {\left(m - 7 \, n + 1\right)} + 3 \, a b^{3} c^{2} d e^{m} n + 4 \, a^{3} b d^{3} e^{m} n\right)} A + {\left(a^{3} b c d^{2} e^{m} {\left(m - 9 \, n + 1\right)} - a b^{3} c^{3} e^{m} {\left(m + 1\right)} - 3 \, a^{2} b^{2} c^{2} d e^{m} n\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left(a^{4} b^{3} c^{5} n^{2} - 3 \, a^{5} b^{2} c^{4} d n^{2} + 3 \, a^{6} b c^{3} d^{2} n^{2} - a^{7} c^{2} d^{3} n^{2} + {\left(a^{2} b^{5} c^{4} d n^{2} - 3 \, a^{3} b^{4} c^{3} d^{2} n^{2} + 3 \, a^{4} b^{3} c^{2} d^{3} n^{2} - a^{5} b^{2} c d^{4} n^{2}\right)} x^{3 \, n} + {\left(a^{2} b^{5} c^{5} n^{2} - a^{3} b^{4} c^{4} d n^{2} - 3 \, a^{4} b^{3} c^{3} d^{2} n^{2} + 5 \, a^{5} b^{2} c^{2} d^{3} n^{2} - 2 \, a^{6} b c d^{4} n^{2}\right)} x^{2 \, n} + {\left(2 \, a^{3} b^{4} c^{5} n^{2} - 5 \, a^{4} b^{3} c^{4} d n^{2} + 3 \, a^{5} b^{2} c^{3} d^{2} n^{2} + a^{6} b c^{2} d^{3} n^{2} - a^{7} c d^{4} n^{2}\right)} x^{n}\right)}}"," ",0,"(((m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*b^4*c^2*e^m - 2*(m^2 - m*(5*n - 2) + 4*n^2 - 5*n + 1)*a*b^3*c*d*e^m + (m^2 - m*(7*n - 2) + 12*n^2 - 7*n + 1)*a^2*b^2*d^2*e^m)*A - ((m^2 - m*(n - 2) - n + 1)*a*b^3*c^2*e^m - 2*(m^2 - m*(3*n - 2) - 3*n + 1)*a^2*b^2*c*d*e^m + (m^2 - m*(5*n - 2) + 6*n^2 - 5*n + 1)*a^3*b*d^2*e^m)*B)*integrate(1/2*x^m/(a^3*b^4*c^4*n^2 - 4*a^4*b^3*c^3*d*n^2 + 6*a^5*b^2*c^2*d^2*n^2 - 4*a^6*b*c*d^3*n^2 + a^7*d^4*n^2 + (a^2*b^5*c^4*n^2 - 4*a^3*b^4*c^3*d*n^2 + 6*a^4*b^3*c^2*d^2*n^2 - 4*a^5*b^2*c*d^3*n^2 + a^6*b*d^4*n^2)*x^n), x) - ((a*d^4*e^m*(m - n + 1) - b*c*d^3*e^m*(m - 4*n + 1))*A + (b*c^2*d^2*e^m*(m - 3*n + 1) - a*c*d^3*e^m*(m + 1))*B)*integrate(x^m/(b^4*c^6*n - 4*a*b^3*c^5*d*n + 6*a^2*b^2*c^4*d^2*n - 4*a^3*b*c^3*d^3*n + a^4*c^2*d^4*n + (b^4*c^5*d*n - 4*a*b^3*c^4*d^2*n + 6*a^2*b^2*c^3*d^3*n - 4*a^3*b*c^2*d^4*n + a^4*c*d^5*n)*x^n), x) - 1/2*(((a*b^3*c^3*e^m*(m - 3*n + 1) - a^2*b^2*c^2*d*e^m*(m - 7*n + 1) + 2*a^4*d^3*e^m*n)*A - (a^2*b^2*c^3*e^m*(m - n + 1) - a^3*b*c^2*d*e^m*(m - 5*n + 1) + 2*a^4*c*d^2*e^m*n)*B)*x*x^m + ((b^4*c^2*d*e^m*(m - 2*n + 1) - a*b^3*c*d^2*e^m*(m - 6*n + 1) + 2*a^2*b^2*d^3*e^m*n)*A + (a^2*b^2*c*d^2*e^m*(m - 6*n + 1) - a*b^3*c^2*d*e^m*(m + 1))*B)*x*e^(m*log(x) + 2*n*log(x)) + ((b^4*c^3*e^m*(m - 2*n + 1) - a^2*b^2*c*d^2*e^m*(m - 7*n + 1) + 3*a*b^3*c^2*d*e^m*n + 4*a^3*b*d^3*e^m*n)*A + (a^3*b*c*d^2*e^m*(m - 9*n + 1) - a*b^3*c^3*e^m*(m + 1) - 3*a^2*b^2*c^2*d*e^m*n)*B)*x*e^(m*log(x) + n*log(x)))/(a^4*b^3*c^5*n^2 - 3*a^5*b^2*c^4*d*n^2 + 3*a^6*b*c^3*d^2*n^2 - a^7*c^2*d^3*n^2 + (a^2*b^5*c^4*d*n^2 - 3*a^3*b^4*c^3*d^2*n^2 + 3*a^4*b^3*c^2*d^3*n^2 - a^5*b^2*c*d^4*n^2)*x^(3*n) + (a^2*b^5*c^5*n^2 - a^3*b^4*c^4*d*n^2 - 3*a^4*b^3*c^3*d^2*n^2 + 5*a^5*b^2*c^2*d^3*n^2 - 2*a^6*b*c*d^4*n^2)*x^(2*n) + (2*a^3*b^4*c^5*n^2 - 5*a^4*b^3*c^4*d*n^2 + 3*a^5*b^2*c^3*d^2*n^2 + a^6*b*c^2*d^3*n^2 - a^7*c*d^4*n^2)*x^n)","F",0
36,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^2*(A+B*x^n)/(c+d*x^n)^3,x, algorithm=""maxima"")","{\left({\left({\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} b^{2} c^{2} d e^{m} - 2 \, {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a b c d^{2} e^{m} + {\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} a^{2} d^{3} e^{m}\right)} A - {\left({\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} b^{2} c^{3} e^{m} - 2 \, {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a b c^{2} d e^{m} + {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a^{2} c d^{2} e^{m}\right)} B\right)} \int \frac{x^{m}}{2 \, {\left(c^{2} d^{4} n^{2} x^{n} + c^{3} d^{3} n^{2}\right)}}\,{d x} + \frac{2 \, B b^{2} c^{2} d^{2} e^{m} n^{2} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} - {\left({\left({\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} b^{2} c^{3} d e^{m} - 2 \, {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a b c^{2} d^{2} e^{m} + {\left(m^{2} - m {\left(3 \, n - 2\right)} - 3 \, n + 1\right)} a^{2} c d^{3} e^{m}\right)} A - {\left({\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} b^{2} c^{4} e^{m} - 2 \, {\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} a b c^{3} d e^{m} + {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a^{2} c^{2} d^{2} e^{m}\right)} B\right)} x x^{m} - {\left({\left({\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} b^{2} c^{2} d^{2} e^{m} - 2 \, {\left(m^{2} + 2 \, m + 1\right)} a b c d^{3} e^{m} + {\left(m^{2} - 2 \, m {\left(n - 1\right)} - 2 \, n + 1\right)} a^{2} d^{4} e^{m}\right)} A - {\left({\left(m^{2} + 2 \, m {\left(2 \, n + 1\right)} + 4 \, n^{2} + 4 \, n + 1\right)} b^{2} c^{3} d e^{m} - 2 \, {\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} a b c^{2} d^{2} e^{m} + {\left(m^{2} + 2 \, m + 1\right)} a^{2} c d^{3} e^{m}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left({\left(m n^{2} + n^{2}\right)} c^{2} d^{5} x^{2 \, n} + 2 \, {\left(m n^{2} + n^{2}\right)} c^{3} d^{4} x^{n} + {\left(m n^{2} + n^{2}\right)} c^{4} d^{3}\right)}}"," ",0,"(((m^2 + m*(n + 2) + n + 1)*b^2*c^2*d*e^m - 2*(m^2 - m*(n - 2) - n + 1)*a*b*c*d^2*e^m + (m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*a^2*d^3*e^m)*A - ((m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*b^2*c^3*e^m - 2*(m^2 + m*(n + 2) + n + 1)*a*b*c^2*d*e^m + (m^2 - m*(n - 2) - n + 1)*a^2*c*d^2*e^m)*B)*integrate(1/2*x^m/(c^2*d^4*n^2*x^n + c^3*d^3*n^2), x) + 1/2*(2*B*b^2*c^2*d^2*e^m*n^2*x*e^(m*log(x) + 2*n*log(x)) - (((m^2 + m*(n + 2) + n + 1)*b^2*c^3*d*e^m - 2*(m^2 - m*(n - 2) - n + 1)*a*b*c^2*d^2*e^m + (m^2 - m*(3*n - 2) - 3*n + 1)*a^2*c*d^3*e^m)*A - ((m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*b^2*c^4*e^m - 2*(m^2 + m*(n + 2) + n + 1)*a*b*c^3*d*e^m + (m^2 - m*(n - 2) - n + 1)*a^2*c^2*d^2*e^m)*B)*x*x^m - (((m^2 + 2*m*(n + 1) + 2*n + 1)*b^2*c^2*d^2*e^m - 2*(m^2 + 2*m + 1)*a*b*c*d^3*e^m + (m^2 - 2*m*(n - 1) - 2*n + 1)*a^2*d^4*e^m)*A - ((m^2 + 2*m*(2*n + 1) + 4*n^2 + 4*n + 1)*b^2*c^3*d*e^m - 2*(m^2 + 2*m*(n + 1) + 2*n + 1)*a*b*c^2*d^2*e^m + (m^2 + 2*m + 1)*a^2*c*d^3*e^m)*B)*x*e^(m*log(x) + n*log(x)))/((m*n^2 + n^2)*c^2*d^5*x^(2*n) + 2*(m*n^2 + n^2)*c^3*d^4*x^n + (m*n^2 + n^2)*c^4*d^3)","F",0
37,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)*(A+B*x^n)/(c+d*x^n)^3,x, algorithm=""maxima"")","-{\left({\left({\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} b c d e^{m} - {\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} a d^{2} e^{m}\right)} A - {\left({\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} b c^{2} e^{m} - {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a c d e^{m}\right)} B\right)} \int \frac{x^{m}}{2 \, {\left(c^{2} d^{3} n^{2} x^{n} + c^{3} d^{2} n^{2}\right)}}\,{d x} + \frac{{\left({\left(b c^{2} d e^{m} {\left(m - n + 1\right)} - a c d^{2} e^{m} {\left(m - 3 \, n + 1\right)}\right)} A - {\left(b c^{3} e^{m} {\left(m + n + 1\right)} - a c^{2} d e^{m} {\left(m - n + 1\right)}\right)} B\right)} x x^{m} - {\left({\left(a d^{3} e^{m} {\left(m - 2 \, n + 1\right)} - b c d^{2} e^{m} {\left(m + 1\right)}\right)} A + {\left(b c^{2} d e^{m} {\left(m + 2 \, n + 1\right)} - a c d^{2} e^{m} {\left(m + 1\right)}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left(c^{2} d^{4} n^{2} x^{2 \, n} + 2 \, c^{3} d^{3} n^{2} x^{n} + c^{4} d^{2} n^{2}\right)}}"," ",0,"-(((m^2 - m*(n - 2) - n + 1)*b*c*d*e^m - (m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*a*d^2*e^m)*A - ((m^2 + m*(n + 2) + n + 1)*b*c^2*e^m - (m^2 - m*(n - 2) - n + 1)*a*c*d*e^m)*B)*integrate(1/2*x^m/(c^2*d^3*n^2*x^n + c^3*d^2*n^2), x) + 1/2*(((b*c^2*d*e^m*(m - n + 1) - a*c*d^2*e^m*(m - 3*n + 1))*A - (b*c^3*e^m*(m + n + 1) - a*c^2*d*e^m*(m - n + 1))*B)*x*x^m - ((a*d^3*e^m*(m - 2*n + 1) - b*c*d^2*e^m*(m + 1))*A + (b*c^2*d*e^m*(m + 2*n + 1) - a*c*d^2*e^m*(m + 1))*B)*x*e^(m*log(x) + n*log(x)))/(c^2*d^4*n^2*x^(2*n) + 2*c^3*d^3*n^2*x^n + c^4*d^2*n^2)","F",0
38,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(c+d*x^n)^3,x, algorithm=""maxima"")","-{\left({\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} B c e^{m} - {\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} A d e^{m}\right)} \int \frac{x^{m}}{2 \, {\left(c^{2} d^{2} n^{2} x^{n} + c^{3} d n^{2}\right)}}\,{d x} + \frac{{\left(B c^{2} e^{m} {\left(m - n + 1\right)} - A c d e^{m} {\left(m - 3 \, n + 1\right)}\right)} x x^{m} - {\left(A d^{2} e^{m} {\left(m - 2 \, n + 1\right)} - B c d e^{m} {\left(m + 1\right)}\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left(c^{2} d^{3} n^{2} x^{2 \, n} + 2 \, c^{3} d^{2} n^{2} x^{n} + c^{4} d n^{2}\right)}}"," ",0,"-((m^2 - m*(n - 2) - n + 1)*B*c*e^m - (m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*A*d*e^m)*integrate(1/2*x^m/(c^2*d^2*n^2*x^n + c^3*d*n^2), x) + 1/2*((B*c^2*e^m*(m - n + 1) - A*c*d*e^m*(m - 3*n + 1))*x*x^m - (A*d^2*e^m*(m - 2*n + 1) - B*c*d*e^m*(m + 1))*x*e^(m*log(x) + n*log(x)))/(c^2*d^3*n^2*x^(2*n) + 2*c^3*d^2*n^2*x^n + c^4*d*n^2)","F",0
39,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(a+b*x^n)/(c+d*x^n)^3,x, algorithm=""maxima"")","{\left({\left({\left(m^{2} - m {\left(5 \, n - 2\right)} + 6 \, n^{2} - 5 \, n + 1\right)} b^{2} c^{2} d e^{m} - 2 \, {\left(m^{2} - 2 \, m {\left(2 \, n - 1\right)} + 3 \, n^{2} - 4 \, n + 1\right)} a b c d^{2} e^{m} + {\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} a^{2} d^{3} e^{m}\right)} A - {\left({\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} b^{2} c^{3} e^{m} - 2 \, {\left(m^{2} - 2 \, m {\left(n - 1\right)} - 2 \, n + 1\right)} a b c^{2} d e^{m} + {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a^{2} c d^{2} e^{m}\right)} B\right)} \int -\frac{x^{m}}{2 \, {\left(b^{3} c^{6} n^{2} - 3 \, a b^{2} c^{5} d n^{2} + 3 \, a^{2} b c^{4} d^{2} n^{2} - a^{3} c^{3} d^{3} n^{2} + {\left(b^{3} c^{5} d n^{2} - 3 \, a b^{2} c^{4} d^{2} n^{2} + 3 \, a^{2} b c^{3} d^{3} n^{2} - a^{3} c^{2} d^{4} n^{2}\right)} x^{n}\right)}}\,{d x} + {\left(B a b^{2} e^{m} - A b^{3} e^{m}\right)} \int -\frac{x^{m}}{a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{n}}\,{d x} - \frac{{\left({\left(a c d^{2} e^{m} {\left(m - 3 \, n + 1\right)} - b c^{2} d e^{m} {\left(m - 5 \, n + 1\right)}\right)} A - {\left(a c^{2} d e^{m} {\left(m - n + 1\right)} - b c^{3} e^{m} {\left(m - 3 \, n + 1\right)}\right)} B\right)} x x^{m} + {\left({\left(a d^{3} e^{m} {\left(m - 2 \, n + 1\right)} - b c d^{2} e^{m} {\left(m - 4 \, n + 1\right)}\right)} A + {\left(b c^{2} d e^{m} {\left(m - 2 \, n + 1\right)} - a c d^{2} e^{m} {\left(m + 1\right)}\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left(b^{2} c^{6} n^{2} - 2 \, a b c^{5} d n^{2} + a^{2} c^{4} d^{2} n^{2} + {\left(b^{2} c^{4} d^{2} n^{2} - 2 \, a b c^{3} d^{3} n^{2} + a^{2} c^{2} d^{4} n^{2}\right)} x^{2 \, n} + 2 \, {\left(b^{2} c^{5} d n^{2} - 2 \, a b c^{4} d^{2} n^{2} + a^{2} c^{3} d^{3} n^{2}\right)} x^{n}\right)}}"," ",0,"(((m^2 - m*(5*n - 2) + 6*n^2 - 5*n + 1)*b^2*c^2*d*e^m - 2*(m^2 - 2*m*(2*n - 1) + 3*n^2 - 4*n + 1)*a*b*c*d^2*e^m + (m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*a^2*d^3*e^m)*A - ((m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*b^2*c^3*e^m - 2*(m^2 - 2*m*(n - 1) - 2*n + 1)*a*b*c^2*d*e^m + (m^2 - m*(n - 2) - n + 1)*a^2*c*d^2*e^m)*B)*integrate(-1/2*x^m/(b^3*c^6*n^2 - 3*a*b^2*c^5*d*n^2 + 3*a^2*b*c^4*d^2*n^2 - a^3*c^3*d^3*n^2 + (b^3*c^5*d*n^2 - 3*a*b^2*c^4*d^2*n^2 + 3*a^2*b*c^3*d^3*n^2 - a^3*c^2*d^4*n^2)*x^n), x) + (B*a*b^2*e^m - A*b^3*e^m)*integrate(-x^m/(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3 + (b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^n), x) - 1/2*(((a*c*d^2*e^m*(m - 3*n + 1) - b*c^2*d*e^m*(m - 5*n + 1))*A - (a*c^2*d*e^m*(m - n + 1) - b*c^3*e^m*(m - 3*n + 1))*B)*x*x^m + ((a*d^3*e^m*(m - 2*n + 1) - b*c*d^2*e^m*(m - 4*n + 1))*A + (b*c^2*d*e^m*(m - 2*n + 1) - a*c*d^2*e^m*(m + 1))*B)*x*e^(m*log(x) + n*log(x)))/(b^2*c^6*n^2 - 2*a*b*c^5*d*n^2 + a^2*c^4*d^2*n^2 + (b^2*c^4*d^2*n^2 - 2*a*b*c^3*d^3*n^2 + a^2*c^2*d^4*n^2)*x^(2*n) + 2*(b^2*c^5*d*n^2 - 2*a*b*c^4*d^2*n^2 + a^2*c^3*d^3*n^2)*x^n)","F",0
40,0,0,0,0.000000," ","integrate((e*x)^m*(A+B*x^n)/(a+b*x^n)^2/(c+d*x^n)^3,x, algorithm=""maxima"")","{\left({\left({\left(m^{2} - m {\left(7 \, n - 2\right)} + 12 \, n^{2} - 7 \, n + 1\right)} b^{2} c^{2} d^{2} e^{m} - 2 \, {\left(m^{2} - m {\left(5 \, n - 2\right)} + 4 \, n^{2} - 5 \, n + 1\right)} a b c d^{3} e^{m} + {\left(m^{2} - m {\left(3 \, n - 2\right)} + 2 \, n^{2} - 3 \, n + 1\right)} a^{2} d^{4} e^{m}\right)} A - {\left({\left(m^{2} - m {\left(5 \, n - 2\right)} + 6 \, n^{2} - 5 \, n + 1\right)} b^{2} c^{3} d e^{m} - 2 \, {\left(m^{2} - m {\left(3 \, n - 2\right)} - 3 \, n + 1\right)} a b c^{2} d^{2} e^{m} + {\left(m^{2} - m {\left(n - 2\right)} - n + 1\right)} a^{2} c d^{3} e^{m}\right)} B\right)} \int \frac{x^{m}}{2 \, {\left(b^{4} c^{7} n^{2} - 4 \, a b^{3} c^{6} d n^{2} + 6 \, a^{2} b^{2} c^{5} d^{2} n^{2} - 4 \, a^{3} b c^{4} d^{3} n^{2} + a^{4} c^{3} d^{4} n^{2} + {\left(b^{4} c^{6} d n^{2} - 4 \, a b^{3} c^{5} d^{2} n^{2} + 6 \, a^{2} b^{2} c^{4} d^{3} n^{2} - 4 \, a^{3} b c^{3} d^{4} n^{2} + a^{4} c^{2} d^{5} n^{2}\right)} x^{n}\right)}}\,{d x} - {\left({\left(b^{4} c e^{m} {\left(m - n + 1\right)} - a b^{3} d e^{m} {\left(m - 4 \, n + 1\right)}\right)} A + {\left(a^{2} b^{2} d e^{m} {\left(m - 3 \, n + 1\right)} - a b^{3} c e^{m} {\left(m + 1\right)}\right)} B\right)} \int \frac{x^{m}}{a^{2} b^{4} c^{4} n - 4 \, a^{3} b^{3} c^{3} d n + 6 \, a^{4} b^{2} c^{2} d^{2} n - 4 \, a^{5} b c d^{3} n + a^{6} d^{4} n + {\left(a b^{5} c^{4} n - 4 \, a^{2} b^{4} c^{3} d n + 6 \, a^{3} b^{3} c^{2} d^{2} n - 4 \, a^{4} b^{2} c d^{3} n + a^{5} b d^{4} n\right)} x^{n}}\,{d x} + \frac{{\left({\left(a^{3} c d^{3} e^{m} {\left(m - 3 \, n + 1\right)} - a^{2} b c^{2} d^{2} e^{m} {\left(m - 7 \, n + 1\right)} + 2 \, b^{3} c^{4} e^{m} n\right)} A - {\left(a^{3} c^{2} d^{2} e^{m} {\left(m - n + 1\right)} - a^{2} b c^{3} d e^{m} {\left(m - 5 \, n + 1\right)} + 2 \, a b^{2} c^{4} e^{m} n\right)} B\right)} x x^{m} + {\left({\left(a^{2} b d^{4} e^{m} {\left(m - 2 \, n + 1\right)} - a b^{2} c d^{3} e^{m} {\left(m - 6 \, n + 1\right)} + 2 \, b^{3} c^{2} d^{2} e^{m} n\right)} A + {\left(a b^{2} c^{2} d^{2} e^{m} {\left(m - 6 \, n + 1\right)} - a^{2} b c d^{3} e^{m} {\left(m + 1\right)}\right)} B\right)} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left(a^{3} d^{4} e^{m} {\left(m - 2 \, n + 1\right)} - a b^{2} c^{2} d^{2} e^{m} {\left(m - 7 \, n + 1\right)} + 4 \, b^{3} c^{3} d e^{m} n + 3 \, a^{2} b c d^{3} e^{m} n\right)} A + {\left(a b^{2} c^{3} d e^{m} {\left(m - 9 \, n + 1\right)} - a^{3} c d^{3} e^{m} {\left(m + 1\right)} - 3 \, a^{2} b c^{2} d^{2} e^{m} n\right)} B\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{2 \, {\left(a^{2} b^{3} c^{7} n^{2} - 3 \, a^{3} b^{2} c^{6} d n^{2} + 3 \, a^{4} b c^{5} d^{2} n^{2} - a^{5} c^{4} d^{3} n^{2} + {\left(a b^{4} c^{5} d^{2} n^{2} - 3 \, a^{2} b^{3} c^{4} d^{3} n^{2} + 3 \, a^{3} b^{2} c^{3} d^{4} n^{2} - a^{4} b c^{2} d^{5} n^{2}\right)} x^{3 \, n} + {\left(2 \, a b^{4} c^{6} d n^{2} - 5 \, a^{2} b^{3} c^{5} d^{2} n^{2} + 3 \, a^{3} b^{2} c^{4} d^{3} n^{2} + a^{4} b c^{3} d^{4} n^{2} - a^{5} c^{2} d^{5} n^{2}\right)} x^{2 \, n} + {\left(a b^{4} c^{7} n^{2} - a^{2} b^{3} c^{6} d n^{2} - 3 \, a^{3} b^{2} c^{5} d^{2} n^{2} + 5 \, a^{4} b c^{4} d^{3} n^{2} - 2 \, a^{5} c^{3} d^{4} n^{2}\right)} x^{n}\right)}}"," ",0,"(((m^2 - m*(7*n - 2) + 12*n^2 - 7*n + 1)*b^2*c^2*d^2*e^m - 2*(m^2 - m*(5*n - 2) + 4*n^2 - 5*n + 1)*a*b*c*d^3*e^m + (m^2 - m*(3*n - 2) + 2*n^2 - 3*n + 1)*a^2*d^4*e^m)*A - ((m^2 - m*(5*n - 2) + 6*n^2 - 5*n + 1)*b^2*c^3*d*e^m - 2*(m^2 - m*(3*n - 2) - 3*n + 1)*a*b*c^2*d^2*e^m + (m^2 - m*(n - 2) - n + 1)*a^2*c*d^3*e^m)*B)*integrate(1/2*x^m/(b^4*c^7*n^2 - 4*a*b^3*c^6*d*n^2 + 6*a^2*b^2*c^5*d^2*n^2 - 4*a^3*b*c^4*d^3*n^2 + a^4*c^3*d^4*n^2 + (b^4*c^6*d*n^2 - 4*a*b^3*c^5*d^2*n^2 + 6*a^2*b^2*c^4*d^3*n^2 - 4*a^3*b*c^3*d^4*n^2 + a^4*c^2*d^5*n^2)*x^n), x) - ((b^4*c*e^m*(m - n + 1) - a*b^3*d*e^m*(m - 4*n + 1))*A + (a^2*b^2*d*e^m*(m - 3*n + 1) - a*b^3*c*e^m*(m + 1))*B)*integrate(x^m/(a^2*b^4*c^4*n - 4*a^3*b^3*c^3*d*n + 6*a^4*b^2*c^2*d^2*n - 4*a^5*b*c*d^3*n + a^6*d^4*n + (a*b^5*c^4*n - 4*a^2*b^4*c^3*d*n + 6*a^3*b^3*c^2*d^2*n - 4*a^4*b^2*c*d^3*n + a^5*b*d^4*n)*x^n), x) + 1/2*(((a^3*c*d^3*e^m*(m - 3*n + 1) - a^2*b*c^2*d^2*e^m*(m - 7*n + 1) + 2*b^3*c^4*e^m*n)*A - (a^3*c^2*d^2*e^m*(m - n + 1) - a^2*b*c^3*d*e^m*(m - 5*n + 1) + 2*a*b^2*c^4*e^m*n)*B)*x*x^m + ((a^2*b*d^4*e^m*(m - 2*n + 1) - a*b^2*c*d^3*e^m*(m - 6*n + 1) + 2*b^3*c^2*d^2*e^m*n)*A + (a*b^2*c^2*d^2*e^m*(m - 6*n + 1) - a^2*b*c*d^3*e^m*(m + 1))*B)*x*e^(m*log(x) + 2*n*log(x)) + ((a^3*d^4*e^m*(m - 2*n + 1) - a*b^2*c^2*d^2*e^m*(m - 7*n + 1) + 4*b^3*c^3*d*e^m*n + 3*a^2*b*c*d^3*e^m*n)*A + (a*b^2*c^3*d*e^m*(m - 9*n + 1) - a^3*c*d^3*e^m*(m + 1) - 3*a^2*b*c^2*d^2*e^m*n)*B)*x*e^(m*log(x) + n*log(x)))/(a^2*b^3*c^7*n^2 - 3*a^3*b^2*c^6*d*n^2 + 3*a^4*b*c^5*d^2*n^2 - a^5*c^4*d^3*n^2 + (a*b^4*c^5*d^2*n^2 - 3*a^2*b^3*c^4*d^3*n^2 + 3*a^3*b^2*c^3*d^4*n^2 - a^4*b*c^2*d^5*n^2)*x^(3*n) + (2*a*b^4*c^6*d*n^2 - 5*a^2*b^3*c^5*d^2*n^2 + 3*a^3*b^2*c^4*d^3*n^2 + a^4*b*c^3*d^4*n^2 - a^5*c^2*d^5*n^2)*x^(2*n) + (a*b^4*c^7*n^2 - a^2*b^3*c^6*d*n^2 - 3*a^3*b^2*c^5*d^2*n^2 + 5*a^4*b*c^4*d^3*n^2 - 2*a^5*c^3*d^4*n^2)*x^n)","F",0
41,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^p*(A+B*x^n)*(c+d*x^n)^q,x, algorithm=""maxima"")","\int {\left(B x^{n} + A\right)} {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{q} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((B*x^n + A)*(b*x^n + a)^p*(d*x^n + c)^q*(e*x)^m, x)","F",0
42,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^p*(A+B*x^n)*(c+d*x^n),x, algorithm=""maxima"")","\int {\left(B x^{n} + A\right)} {\left(d x^{n} + c\right)} {\left(b x^{n} + a\right)}^{p} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((B*x^n + A)*(d*x^n + c)*(b*x^n + a)^p*(e*x)^m, x)","F",0
43,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^p*(A+B*x^n)/(c+d*x^n),x, algorithm=""maxima"")","\int \frac{{\left(B x^{n} + A\right)} {\left(b x^{n} + a\right)}^{p} \left(e x\right)^{m}}{d x^{n} + c}\,{d x}"," ",0,"integrate((B*x^n + A)*(b*x^n + a)^p*(e*x)^m/(d*x^n + c), x)","F",0
44,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*x^n)^p*(A+B*x^n)/(c+d*x^n)^2,x, algorithm=""maxima"")","\int \frac{{\left(B x^{n} + A\right)} {\left(b x^{n} + a\right)}^{p} \left(e x\right)^{m}}{{\left(d x^{n} + c\right)}^{2}}\,{d x}"," ",0,"integrate((B*x^n + A)*(b*x^n + a)^p*(e*x)^m/(d*x^n + c)^2, x)","F",0
45,0,0,0,0.000000," ","integrate((-a+b*x^(1/2*n))^(-1+1/n)*(a+b*x^(1/2*n))^(-1+1/n)*(c+d*x^n)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{n} + c\right)} {\left(b x^{\frac{1}{2} \, n} + a\right)}^{\frac{1}{n} - 1} {\left(b x^{\frac{1}{2} \, n} - a\right)}^{\frac{1}{n} - 1}}{x^{2}}\,{d x}"," ",0,"integrate((d*x^n + c)*(b*x^(1/2*n) + a)^(1/n - 1)*(b*x^(1/2*n) - a)^(1/n - 1)/x^2, x)","F",0
46,0,0,0,0.000000," ","integrate((-a+b*x^(1/2*n))^((1-n)/n)*(a+b*x^(1/2*n))^((1-n)/n)*(c+d*x^n)/x^2,x, algorithm=""maxima"")","\int \frac{d x^{n} + c}{{\left(b x^{\frac{1}{2} \, n} + a\right)}^{\frac{n - 1}{n}} {\left(b x^{\frac{1}{2} \, n} - a\right)}^{\frac{n - 1}{n}} x^{2}}\,{d x}"," ",0,"integrate((d*x^n + c)/((b*x^(1/2*n) + a)^((n - 1)/n)*(b*x^(1/2*n) - a)^((n - 1)/n)*x^2), x)","F",0
