# Maple integration test file: "1 Algebraic functions\1.1 Binomial products\1.1.3 General\1.1.3.6 (g x)^m (a+b x^n)^p (c+d x^n)^q (e+f x^n)^r.txt"

lst:=[

# Integrands of the form (g x)^m (a+b x^n)^p (c+d x^n)^q (e+f x^n)^r

# Integrands of the form (e x)^m (a+b x^n)^p (c+d x^n)^q (A+B x^n)

# Integrands of the form (e x)^m (a+b x^n)^p (c+d x^n)^q (A+B x^n)

# q>0
[(e*x)^m*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n),x,12,a^2*(3*A*b*c+a*B*c+a*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+a*(3*A*b*(b*c+a*d)+a*B*(3*b*c+a*d))*x^(1+2*n)*(e*x)^m/(1+m+2*n)+b*(3*a*B*(b*c+a*d)+A*b*(b*c+3*a*d))*x^(1+3*n)*(e*x)^m/(1+m+3*n)+b^2*(b*B*c+A*b*d+3*a*B*d)*x^(1+4*n)*(e*x)^m/(1+m+4*n)+b^3*B*d*x^(1+5*n)*(e*x)^m/(1+m+5*n)+a^3*A*c*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(a+b*x^n)^2*(A+B*x^n)*(c+d*x^n),x,10,a*(2*A*b*c+a*B*c+a*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+(a*B*(2*b*c+a*d)+A*b*(b*c+2*a*d))*x^(1+2*n)*(e*x)^m/(1+m+2*n)+b*(b*B*c+A*b*d+2*a*B*d)*x^(1+3*n)*(e*x)^m/(1+m+3*n)+b^2*B*d*x^(1+4*n)*(e*x)^m/(1+m+4*n)+a^2*A*c*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(a+b*x^n)*(A+B*x^n)*(c+d*x^n),x,8,(A*b*c+a*B*c+a*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+(b*B*c+A*b*d+a*B*d)*x^(1+2*n)*(e*x)^m/(1+m+2*n)+b*B*d*x^(1+3*n)*(e*x)^m/(1+m+3*n)+a*A*c*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n),x,6,(B*c+A*d)*x^(1+n)*(e*x)^m/(1+m+n)+B*d*x^(1+2*n)*(e*x)^m/(1+m+2*n)+A*c*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)/(a+b*x^n),x,5,B*d*x^(1+n)*(e*x)^m/(b*(1+m+n))+(b*B*c+A*b*d-a*B*d)*(e*x)^(1+m)/(b^2*e*(1+m))+(A*b-a*B)*(b*c-a*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a*b^2*e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)/(a+b*x^n)^2,x,3,-d*(A*b*(1+m)-a*B*(1+m+n))*(e*x)^(1+m)/(a*b^2*e*(1+m)*n)+(A*b-a*B)*(e*x)^(1+m)*(c+d*x^n)/(a*b*e*n*(a+b*x^n))+(b*c*(a*B*(1+m)-A*b*(1+m-n))+a*d*(A*b*(1+m)-a*B*(1+m+n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^2*b^2*e*(1+m)*n)],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)/(a+b*x^n)^3,x,3,-1/2*(A*b*(b*c*(1+m-2*n)-a*d*(1+m-n))-a*B*(b*c*(1+m)-a*d*(1+m+n)))*(e*x)^(1+m)/(a^2*b^2*e*n^2*(a+b*x^n))+1/2*(A*b-a*B)*(e*x)^(1+m)*(c+d*x^n)/(a*b*e*n*(a+b*x^n)^2)-1/2*(b*c*(a*B*(1+m)-A*b*(1+m-2*n))*(1+m-n)+a*d*(1+m)*(A*b*(1+m-n)-a*B*(1+m+n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^3*b^2*e*(1+m)*n^2)],
[(e*x)^m*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n)^2,x,14,a^2*c*(3*A*b*c+a*B*c+2*a*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+a*(a*B*c*(3*b*c+2*a*d)+A*(3*b^2*c^2+6*a*b*c*d+a^2*d^2))*x^(1+2*n)*(e*x)^m/(1+m+2*n)+(a*B*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)+A*b*(b^2*c^2+6*a*b*c*d+3*a^2*d^2))*x^(1+3*n)*(e*x)^m/(1+m+3*n)+b*(3*a^2*B*d^2+3*a*b*d*(2*B*c+A*d)+b^2*c*(B*c+2*A*d))*x^(1+4*n)*(e*x)^m/(1+m+4*n)+b^2*d*(2*b*B*c+A*b*d+3*a*B*d)*x^(1+5*n)*(e*x)^m/(1+m+5*n)+b^3*B*d^2*x^(1+6*n)*(e*x)^m/(1+m+6*n)+a^3*A*c^2*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(a+b*x^n)^2*(A+B*x^n)*(c+d*x^n)^2,x,12,a*c*(a*B*c+2*A*(b*c+a*d))*x^(1+n)*(e*x)^m/(1+m+n)+(2*a*B*c*(b*c+a*d)+A*(b^2*c^2+4*a*b*c*d+a^2*d^2))*x^(1+2*n)*(e*x)^m/(1+m+2*n)+(a^2*B*d^2+2*a*b*d*(2*B*c+A*d)+b^2*c*(B*c+2*A*d))*x^(1+3*n)*(e*x)^m/(1+m+3*n)+b*d*(2*b*B*c+A*b*d+2*a*B*d)*x^(1+4*n)*(e*x)^m/(1+m+4*n)+b^2*B*d^2*x^(1+5*n)*(e*x)^m/(1+m+5*n)+a^2*A*c^2*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(a+b*x^n)*(A+B*x^n)*(c+d*x^n)^2,x,10,c*(A*b*c+a*B*c+2*a*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+(a*d*(2*B*c+A*d)+b*c*(B*c+2*A*d))*x^(1+2*n)*(e*x)^m/(1+m+2*n)+d*(2*b*B*c+A*b*d+a*B*d)*x^(1+3*n)*(e*x)^m/(1+m+3*n)+b*B*d^2*x^(1+4*n)*(e*x)^m/(1+m+4*n)+a*A*c^2*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)^2,x,8,c*(B*c+2*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+d*(2*B*c+A*d)*x^(1+2*n)*(e*x)^m/(1+m+2*n)+B*d^2*x^(1+3*n)*(e*x)^m/(1+m+3*n)+A*c^2*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)^2/(a+b*x^n),x,7,d*(2*b*B*c+A*b*d-a*B*d)*x^(1+n)*(e*x)^m/(b^2*(1+m+n))+B*d^2*x^(1+2*n)*(e*x)^m/(b*(1+m+2*n))+(a^2*B*d^2-a*b*d*(2*B*c+A*d)+b^2*c*(B*c+2*A*d))*(e*x)^(1+m)/(b^3*e*(1+m))+(A*b-a*B)*(b*c-a*d)^2*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a*b^3*e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)^2/(a+b*x^n)^2,x,6,-d^2*(A*b*(1+m+n)-a*B*(1+m+2*n))*x^(1+n)*(e*x)^m/(a*b^2*n*(1+m+n))-d*(A*b*(2*b*c*(1+m)-a*d*(1+m+n))-a*B*(2*b*c*(1+m+n)-a*d*(1+m+2*n)))*(e*x)^(1+m)/(a*b^3*e*(1+m)*n)+(A*b-a*B)*(e*x)^(1+m)*(c+d*x^n)^2/(a*b*e*n*(a+b*x^n))-(b*c-a*d)*(A*b*(b*c*(1+m-n)-a*d*(1+m+n))-a*B*(b*c*(1+m)-a*d*(1+m+2*n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^2*b^3*e*(1+m)*n)],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)^2/(a+b*x^n)^3,x,4,1/2*d*(b*c*(1+m)-a*d*(1+m+n))*(A*b*(1+m)-a*B*(1+m+2*n))*(e*x)^(1+m)/(a^2*b^3*e*(1+m)*n^2)+1/2*(A*b-a*B)*(e*x)^(1+m)*(c+d*x^n)^2/(a*b*e*n*(a+b*x^n)^2)+1/2*(b*c-a*d)*(e*x)^(1+m)*(c*(a*B*(1+m)-A*b*(1+m-2*n))-d*(A*b*(1+m)-a*B*(1+m+2*n))*x^n)/(a^2*b^2*e*n^2*(a+b*x^n))+1/2*(b*c*(a*B*(1+m)-A*b*(1+m-2*n))*(a*d*(1+m)-b*c*(1+m-n))-a*d*(b*c*(1+m)-a*d*(1+m+n))*(A*b*(1+m)-a*B*(1+m+2*n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^3*b^3*e*(1+m)*n^2)],
[(e*x)^m*(a+b*x^n)^3*(A+B*x^n)*(c+d*x^n)^3,x,16,a^2*c^2*(a*B*c+3*A*(b*c+a*d))*x^(1+n)*(e*x)^m/(1+m+n)+3*a*c*(a*B*c*(b*c+a*d)+A*(b^2*c^2+3*a*b*c*d+a^2*d^2))*x^(1+2*n)*(e*x)^m/(1+m+2*n)+(3*a*B*c*(b^2*c^2+3*a*b*c*d+a^2*d^2)+A*(b^3*c^3+9*a*b^2*c^2*d+9*a^2*b*c*d^2+a^3*d^3))*x^(1+3*n)*(e*x)^m/(1+m+3*n)+(a^3*B*d^3+9*a*b^2*c*d*(B*c+A*d)+3*a^2*b*d^2*(3*B*c+A*d)+b^3*c^2*(B*c+3*A*d))*x^(1+4*n)*(e*x)^m/(1+m+4*n)+3*b*d*(a^2*B*d^2+b^2*c*(B*c+A*d)+a*b*d*(3*B*c+A*d))*x^(1+5*n)*(e*x)^m/(1+m+5*n)+b^2*d^2*(3*b*B*c+A*b*d+3*a*B*d)*x^(1+6*n)*(e*x)^m/(1+m+6*n)+b^3*B*d^3*x^(1+7*n)*(e*x)^m/(1+m+7*n)+a^3*A*c^3*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(a+b*x^n)^2*(A+B*x^n)*(c+d*x^n)^3,x,14,a*c^2*(2*A*b*c+a*B*c+3*a*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+c*(a*B*c*(2*b*c+3*a*d)+A*(b^2*c^2+6*a*b*c*d+3*a^2*d^2))*x^(1+2*n)*(e*x)^m/(1+m+2*n)+(6*a*b*c*d*(B*c+A*d)+a^2*d^2*(3*B*c+A*d)+b^2*c^2*(B*c+3*A*d))*x^(1+3*n)*(e*x)^m/(1+m+3*n)+d*(a^2*B*d^2+3*b^2*c*(B*c+A*d)+2*a*b*d*(3*B*c+A*d))*x^(1+4*n)*(e*x)^m/(1+m+4*n)+b*d^2*(3*b*B*c+A*b*d+2*a*B*d)*x^(1+5*n)*(e*x)^m/(1+m+5*n)+b^2*B*d^3*x^(1+6*n)*(e*x)^m/(1+m+6*n)+a^2*A*c^3*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(a+b*x^n)*(A+B*x^n)*(c+d*x^n)^3,x,12,c^2*(A*b*c+a*B*c+3*a*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+c*(3*a*d*(B*c+A*d)+b*c*(B*c+3*A*d))*x^(1+2*n)*(e*x)^m/(1+m+2*n)+d*(3*b*c*(B*c+A*d)+a*d*(3*B*c+A*d))*x^(1+3*n)*(e*x)^m/(1+m+3*n)+d^2*(3*b*B*c+A*b*d+a*B*d)*x^(1+4*n)*(e*x)^m/(1+m+4*n)+b*B*d^3*x^(1+5*n)*(e*x)^m/(1+m+5*n)+a*A*c^3*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)^3,x,10,c^2*(B*c+3*A*d)*x^(1+n)*(e*x)^m/(1+m+n)+3*c*d*(B*c+A*d)*x^(1+2*n)*(e*x)^m/(1+m+2*n)+d^2*(3*B*c+A*d)*x^(1+3*n)*(e*x)^m/(1+m+3*n)+B*d^3*x^(1+4*n)*(e*x)^m/(1+m+4*n)+A*c^3*(e*x)^(1+m)/(e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)^3/(a+b*x^n),x,9,d*(a^2*B*d^2+3*b^2*c*(B*c+A*d)-a*b*d*(3*B*c+A*d))*x^(1+n)*(e*x)^m/(b^3*(1+m+n))+d^2*(3*b*B*c+A*b*d-a*B*d)*x^(1+2*n)*(e*x)^m/(b^2*(1+m+2*n))+B*d^3*x^(1+3*n)*(e*x)^m/(b*(1+m+3*n))-(a^3*B*d^3+3*a*b^2*c*d*(B*c+A*d)-a^2*b*d^2*(3*B*c+A*d)-b^3*c^2*(B*c+3*A*d))*(e*x)^(1+m)/(b^4*e*(1+m))+(A*b-a*B)*(b*c-a*d)^3*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a*b^4*e*(1+m))],
[(e*x)^m*(A+B*x^n)*(c+d*x^n)^3/(a+b*x^n)^2,x,8,-d^2*(A*b*(3*b*c*(1+m+n)-a*d*(1+m+2*n))-a*B*(3*b*c*(1+m+2*n)-a*d*(1+m+3*n)))*x^(1+n)*(e*x)^m/(a*b^3*n*(1+m+n))-d^3*(A*b*(1+m+2*n)-a*B*(1+m+3*n))*x^(1+2*n)*(e*x)^m/(a*b^2*n*(1+m+2*n))-d*(A*b*(3*b^2*c^2*(1+m)-3*a*b*c*d*(1+m+n)+a^2*d^2*(1+m+2*n))-a*B*(3*b^2*c^2*(1+m+n)-3*a*b*c*d*(1+m+2*n)+a^2*d^2*(1+m+3*n)))*(e*x)^(1+m)/(a*b^4*e*(1+m)*n)+(A*b-a*B)*(e*x)^(1+m)*(c+d*x^n)^3/(a*b*e*n*(a+b*x^n))-(b*c-a*d)^2*(A*b*(b*c*(1+m-n)-a*d*(1+m+2*n))-a*B*(b*c*(1+m)-a*d*(1+m+3*n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^2*b^4*e*(1+m)*n)],

#  {(e*x)^m/(a + b*x^n)^3*(c + d*x^n)^3*(A + B*x^n), x, 7, (B*d^3*x^(1 + n)*(e*x)^m)/(b^3*(1 + m + n)) + (d^2*(3*b*B*c + A*b*d - 3*a*B*d)*(e*x)^(1 + m))/(b^4*e*(1 + m)) + (3*d*(b*c - a*d)*(b*B*c + A*b*d - 2*a*B*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*b^4*e*(1 + m)) + ((b*c - a*d)^2*(b*B*c + 3*A*b*d - 4*a*B*d)*(e*x)^(1 + m)*Hypergeometric2F1[2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*b^4*e*(1 + m)) + ((A*b - a*B)*(b*c - a*d)^3*(e*x)^(1 + m)*Hypergeometric2F1[3, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^3*b^4*e*(1 + m))}

# q<0
[(e*x)^m*(a+b*x^n)^4*(A+B*x^n)/(c+d*x^n),x,11,b*(4*a^3*B*d^3-b^3*c^2*(B*c-A*d)+4*a*b^2*c*d*(B*c-A*d)-6*a^2*b*d^2*(B*c-A*d))*x^(1+n)*(e*x)^m/(d^4*(1+m+n))+b^2*(6*a^2*B*d^2+b^2*c*(B*c-A*d)-4*a*b*d*(B*c-A*d))*x^(1+2*n)*(e*x)^m/(d^3*(1+m+2*n))-b^3*(b*B*c-A*b*d-4*a*B*d)*x^(1+3*n)*(e*x)^m/(d^2*(1+m+3*n))+b^4*B*x^(1+4*n)*(e*x)^m/(d*(1+m+4*n))+(a^4*B*d^4+b^4*c^3*(B*c-A*d)-4*a*b^3*c^2*d*(B*c-A*d)+6*a^2*b^2*c*d^2*(B*c-A*d)-4*a^3*b*d^3*(B*c-A*d))*(e*x)^(1+m)/(d^5*e*(1+m))-(b*c-a*d)^4*(B*c-A*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*d^5*e*(1+m))],
[(e*x)^m*(a+b*x^n)^3*(A+B*x^n)/(c+d*x^n),x,9,b*(3*a^2*B*d^2+b^2*c*(B*c-A*d)-3*a*b*d*(B*c-A*d))*x^(1+n)*(e*x)^m/(d^3*(1+m+n))-b^2*(b*B*c-A*b*d-3*a*B*d)*x^(1+2*n)*(e*x)^m/(d^2*(1+m+2*n))+b^3*B*x^(1+3*n)*(e*x)^m/(d*(1+m+3*n))+(a^3*B*d^3-b^3*c^2*(B*c-A*d)+3*a*b^2*c*d*(B*c-A*d)-3*a^2*b*d^2*(B*c-A*d))*(e*x)^(1+m)/(d^4*e*(1+m))+(b*c-a*d)^3*(B*c-A*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*d^4*e*(1+m))],
[(e*x)^m*(a+b*x^n)^2*(A+B*x^n)/(c+d*x^n),x,7,-b*(b*B*c-A*b*d-2*a*B*d)*x^(1+n)*(e*x)^m/(d^2*(1+m+n))+b^2*B*x^(1+2*n)*(e*x)^m/(d*(1+m+2*n))+(a^2*B*d^2+b^2*c*(B*c-A*d)-2*a*b*d*(B*c-A*d))*(e*x)^(1+m)/(d^3*e*(1+m))-(b*c-a*d)^2*(B*c-A*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*d^3*e*(1+m))],
[(e*x)^m*(a+b*x^n)*(A+B*x^n)/(c+d*x^n),x,5,b*B*x^(1+n)*(e*x)^m/(d*(1+m+n))-(b*B*c-A*b*d-a*B*d)*(e*x)^(1+m)/(d^2*e*(1+m))+(b*c-a*d)*(B*c-A*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*d^2*e*(1+m))],
[(e*x)^m*(A+B*x^n)/(c+d*x^n),x,2,B*(e*x)^(1+m)/(d*e*(1+m))-(B*c-A*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*d*e*(1+m))],
[(e*x)^m*(A+B*x^n)/((a+b*x^n)*(c+d*x^n)),x,4,(A*b-a*B)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a*(b*c-a*d)*e*(1+m))+(B*c-A*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*(b*c-a*d)*e*(1+m))],
[(e*x)^m*(A+B*x^n)/((a+b*x^n)^2*(c+d*x^n)),x,5,(A*b-a*B)*(e*x)^(1+m)/(a*(b*c-a*d)*e*n*(a+b*x^n))+(A*b*(a*d*(1+m-2*n)-b*c*(1+m-n))+a*B*(b*c*(1+m)-a*d*(1+m-n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^2*(b*c-a*d)^2*e*(1+m)*n)-d*(B*c-A*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*(b*c-a*d)^2*e*(1+m))],
[(e*x)^m*(A+B*x^n)/((a+b*x^n)^3*(c+d*x^n)),x,6,1/2*(A*b-a*B)*(e*x)^(1+m)/(a*(b*c-a*d)*e*n*(a+b*x^n)^2)+1/2*(A*b*(a*d*(1+m-4*n)-b*c*(1+m-2*n))+a*B*(b*c*(1+m)-a*d*(1+m-2*n)))*(e*x)^(1+m)/(a^2*(b*c-a*d)^2*e*n^2*(a+b*x^n))+1/2*(a*B*(2*a*b*c*d*(1+m)*(1+m-2*n)-b^2*c^2*(1+m)*(1+m-n)-a^2*d^2*(1+m^2+m*(2-3*n)-3*n+2*n^2))+A*b*(b^2*c^2*(1+m^2+m*(2-3*n)-3*n+2*n^2)-2*a*b*c*d*(1+m^2+m*(2-4*n)-4*n+3*n^2)+a^2*d^2*(1+m^2+m*(2-5*n)-5*n+6*n^2)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^3*(b*c-a*d)^3*e*(1+m)*n^2)+d^2*(B*c-A*d)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*(b*c-a*d)^3*e*(1+m))],
[(e*x)^m*(a+b*x^n)^3*(A+B*x^n)/(c+d*x^n)^2,x,8,-b^2*(3*a*d*(A*d*(1+m+n)-B*c*(1+m+2*n))-b*c*(A*d*(1+m+2*n)-B*c*(1+m+3*n)))*x^(1+n)*(e*x)^m/(c*d^3*n*(1+m+n))-b^3*(A*d*(1+m+2*n)-B*c*(1+m+3*n))*x^(1+2*n)*(e*x)^m/(c*d^2*n*(1+m+2*n))-b*(3*a^2*d^2*(A*d*(1+m)-B*c*(1+m+n))-3*a*b*c*d*(A*d*(1+m+n)-B*c*(1+m+2*n))+b^2*c^2*(A*d*(1+m+2*n)-B*c*(1+m+3*n)))*(e*x)^(1+m)/(c*d^4*e*(1+m)*n)-(B*c-A*d)*(e*x)^(1+m)*(a+b*x^n)^3/(c*d*e*n*(c+d*x^n))+(b*c-a*d)^2*(a*d*(B*c*(1+m)-A*d*(1+m-n))+b*c*(A*d*(1+m+2*n)-B*c*(1+m+3*n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^2*d^4*e*(1+m)*n)],
[(e*x)^m*(a+b*x^n)^2*(A+B*x^n)/(c+d*x^n)^2,x,6,-b^2*(A*d*(1+m+n)-B*c*(1+m+2*n))*x^(1+n)*(e*x)^m/(c*d^2*n*(1+m+n))-b*(2*a*d*(A*d*(1+m)-B*c*(1+m+n))-b*c*(A*d*(1+m+n)-B*c*(1+m+2*n)))*(e*x)^(1+m)/(c*d^3*e*(1+m)*n)-(B*c-A*d)*(e*x)^(1+m)*(a+b*x^n)^2/(c*d*e*n*(c+d*x^n))-(b*c-a*d)*(a*d*(B*c*(1+m)-A*d*(1+m-n))+b*c*(A*d*(1+m+n)-B*c*(1+m+2*n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^2*d^3*e*(1+m)*n)],
[(e*x)^m*(a+b*x^n)*(A+B*x^n)/(c+d*x^n)^2,x,3,-B*(a*d*(1+m)-b*c*(1+m+n))*(e*x)^(1+m)/(c*d^2*e*(1+m)*n)-(b*c-a*d)*(e*x)^(1+m)*(A+B*x^n)/(c*d*e*n*(c+d*x^n))+(A*d*(b*c*(1+m)-a*d*(1+m-n))+B*c*(a*d*(1+m)-b*c*(1+m+n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^2*d^2*e*(1+m)*n)],
[(e*x)^m*(A+B*x^n)/(c+d*x^n)^2,x,2,-(B*c-A*d)*(e*x)^(1+m)/(c*d*e*n*(c+d*x^n))+(B*c*(1+m)-A*d*(1+m-n))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^2*d*e*(1+m)*n)],
[(e*x)^m*(A+B*x^n)/((a+b*x^n)*(c+d*x^n)^2),x,5,(B*c-A*d)*(e*x)^(1+m)/(c*(b*c-a*d)*e*n*(c+d*x^n))+b*(A*b-a*B)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a*(b*c-a*d)^2*e*(1+m))+(b*c*(A*d*(1+m-2*n)-B*c*(1+m-n))+a*d*(B*c*(1+m)-A*d*(1+m-n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^2*(b*c-a*d)^2*e*(1+m)*n)],
[(e*x)^m*(A+B*x^n)/((a+b*x^n)^2*(c+d*x^n)^2),x,6,d*(A*b*c-2*a*B*c+a*A*d)*(e*x)^(1+m)/(a*c*(b*c-a*d)^2*e*n*(c+d*x^n))+(A*b-a*B)*(e*x)^(1+m)/(a*(b*c-a*d)*e*n*(a+b*x^n)*(c+d*x^n))+b*(a*B*(b*c*(1+m)-a*d*(1+m-2*n))+A*b*(a*d*(1+m-3*n)-b*c*(1+m-n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^2*(b*c-a*d)^3*e*(1+m)*n)-d*(b*c*(A*d*(1+m-3*n)-B*c*(1+m-2*n))+a*d*(B*c*(1+m)-A*d*(1+m-n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^2*(b*c-a*d)^3*e*(1+m)*n)],
[(e*x)^m*(A+B*x^n)/((a+b*x^n)^3*(c+d*x^n)^2),x,7,1/2*d*(a*B*c*(b*c*(1+m)-a*d*(1+m-6*n))+A*(a*b*c*d*(1+m-6*n)-b^2*c^2*(1+m-2*n)-2*a^2*d^2*n))*(e*x)^(1+m)/(a^2*c*(b*c-a*d)^3*e*n^2*(c+d*x^n))+1/2*(A*b-a*B)*(e*x)^(1+m)/(a*(b*c-a*d)*e*n*(a+b*x^n)^2*(c+d*x^n))+1/2*(a*B*(b*c*(1+m)-a*d*(1+m-3*n))+A*b*(a*d*(1+m-5*n)-b*c*(1+m-2*n)))*(e*x)^(1+m)/(a^2*(b*c-a*d)^2*e*n^2*(a+b*x^n)*(c+d*x^n))+1/2*b*(a*B*(2*a*b*c*d*(1+m)*(1+m-3*n)-b^2*c^2*(1+m)*(1+m-n)-a^2*d^2*(1+m^2+m*(2-5*n)-5*n+6*n^2))+A*b*(b^2*c^2*(1+m^2+m*(2-3*n)-3*n+2*n^2)-2*a*b*c*d*(1+m^2+m*(2-5*n)-5*n+4*n^2)+a^2*d^2*(1+m^2+m*(2-7*n)-7*n+12*n^2)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^3*(b*c-a*d)^4*e*(1+m)*n^2)+d^2*(b*c*(A*d*(1+m-4*n)-B*c*(1+m-3*n))+a*d*(B*c*(1+m)-A*d*(1+m-n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^2*(b*c-a*d)^4*e*(1+m)*n)],

#  {(e*x)^m*(a + b*x^n)^3*(A + B*x^n)/(c + d*x^n)^3, x, 7, (b^3*B*x^(1 + n)*(e*x)^m)/(d^3*(1 + m + n)) - (b^2*(3*b*B*c - A*b*d - 3*a*B*d)*(e*x)^(1 + m))/(d^4*e*(1 + m)) + (3*b*(b*c - a*d)*(2*b*B*c - A*b*d - a*B*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*d^4*e*(1 + m)) - ((b*c - a*d)^2*(4*b*B*c - 3*A*b*d - a*B*d)*(e*x)^(1 + m)*Hypergeometric2F1[2, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*d^4*e*(1 + m)) + ((b*c - a*d)^3*(B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[3, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^3*d^4*e*(1 + m))} 
[(e*x)^m*(a+b*x^n)^2*(A+B*x^n)/(c+d*x^n)^3,x,4,1/2*b*(a*d*(1+m)-b*c*(1+m+n))*(A*d*(1+m)-B*c*(1+m+2*n))*(e*x)^(1+m)/(c^2*d^3*e*(1+m)*n^2)-1/2*(B*c-A*d)*(e*x)^(1+m)*(a+b*x^n)^2/(c*d*e*n*(c+d*x^n)^2)-1/2*(b*c-a*d)*(e*x)^(1+m)*(a*(B*c*(1+m)-A*d*(1+m-2*n))-b*(A*d*(1+m)-B*c*(1+m+2*n))*x^n)/(c^2*d^2*e*n^2*(c+d*x^n))+1/2*(a*d*(B*c*(1+m)-A*d*(1+m-2*n))*(b*c*(1+m)-a*d*(1+m-n))-b*c*(a*d*(1+m)-b*c*(1+m+n))*(A*d*(1+m)-B*c*(1+m+2*n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^3*d^3*e*(1+m)*n^2)],
[(e*x)^m*(a+b*x^n)*(A+B*x^n)/(c+d*x^n)^3,x,3,-1/2*(b*c-a*d)*(e*x)^(1+m)*(A+B*x^n)/(c*d*e*n*(c+d*x^n)^2)-1/2*(a*d*(A*d*(1+m-2*n)-B*c*(1+m-n))-b*c*(A*d*(1+m)-B*c*(1+m+n)))*(e*x)^(1+m)/(c^2*d^2*e*n^2*(c+d*x^n))-1/2*(A*d*(b*c*(1+m)-a*d*(1+m-2*n))*(1+m-n)+B*c*(1+m)*(a*d*(1+m-n)-b*c*(1+m+n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^3*d^2*e*(1+m)*n^2)],
[(e*x)^m*(A+B*x^n)/(c+d*x^n)^3,x,2,-1/2*(B*c-A*d)*(e*x)^(1+m)/(c*d*e*n*(c+d*x^n)^2)+1/2*(B*c*(1+m)-A*d*(1+m-2*n))*(e*x)^(1+m)*hypergeom([2,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^3*d*e*(1+m)*n)],
[(e*x)^m*(A+B*x^n)/((a+b*x^n)*(c+d*x^n)^3),x,6,1/2*(B*c-A*d)*(e*x)^(1+m)/(c*(b*c-a*d)*e*n*(c+d*x^n)^2)+1/2*(b*c*(A*d*(1+m-4*n)-B*c*(1+m-2*n))+a*d*(B*c*(1+m)-A*d*(1+m-2*n)))*(e*x)^(1+m)/(c^2*(b*c-a*d)^2*e*n^2*(c+d*x^n))+b^2*(A*b-a*B)*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a*(b*c-a*d)^3*e*(1+m))-1/2*(b^2*c^2*(A*d*(1+m-3*n)-B*c*(1+m-n))*(1+m-2*n)-a^2*d^2*(B*c*(1+m)-A*d*(1+m-2*n))*(1+m-n)+2*a*b*c*d*(B*c*(1+m)*(1+m-2*n)-A*d*(1+m^2+m*(2-4*n)-4*n+3*n^2)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^3*(b*c-a*d)^3*e*(1+m)*n^2)],
[(e*x)^m*(A+B*x^n)/((a+b*x^n)^2*(c+d*x^n)^3),x,7,1/2*d*(2*A*b*c-3*a*B*c+a*A*d)*(e*x)^(1+m)/(a*c*(b*c-a*d)^2*e*n*(c+d*x^n)^2)+(A*b-a*B)*(e*x)^(1+m)/(a*(b*c-a*d)*e*n*(a+b*x^n)*(c+d*x^n)^2)-1/2*d*(a^2*d*(B*c*(1+m)-A*d*(1+m-2*n))-a*b*c*(B*c-A*d)*(1+m-6*n)-2*A*b^2*c^2*n)*(e*x)^(1+m)/(a*c^2*(b*c-a*d)^3*e*n^2*(c+d*x^n))+b^2*(a*B*(b*c*(1+m)-a*d*(1+m-3*n))+A*b*(a*d*(1+m-4*n)-b*c*(1+m-n)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^2*(b*c-a*d)^4*e*(1+m)*n)+1/2*d*(b^2*c^2*(A*d*(1+m-4*n)-B*c*(1+m-2*n))*(1+m-3*n)-a^2*d^2*(B*c*(1+m)-A*d*(1+m-2*n))*(1+m-n)+2*a*b*c*d*(B*c*(1+m)*(1+m-3*n)-A*d*(1+m^2+m*(2-5*n)-5*n+4*n^2)))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c^3*(b*c-a*d)^4*e*(1+m)*n^2)],

#  {(e*x)^m/(a + b*x^n)^3*(A + B*x^n)/(c + d*x^n)^3, x, 8, -((3*b^2*d*(b*B*c - 2*A*b*d + a*B*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*(b*c - a*d)^5*e*(1 + m))) + (3*b*d^2*(b*B*c - 2*A*b*d + a*B*d)*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*(b*c - a*d)^5*e*(1 + m)) + (b^2*(b*B*c - 3*A*b*d + 2*a*B*d)*(e*x)^(1 + m)*Hypergeometric2F1[2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*(b*c - a*d)^4*e*(1 + m)) + (d^2*(2*b*B*c - 3*A*b*d + a*B*d)*(e*x)^(1 + m)*Hypergeometric2F1[2, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^2*(b*c - a*d)^4*e*(1 + m)) + (b^2*(A*b - a*B)*(e*x)^(1 + m)*Hypergeometric2F1[3, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^3*(b*c - a*d)^3*e*(1 + m)) + (d^2*(B*c - A*d)*(e*x)^(1 + m)*Hypergeometric2F1[3, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c^3*(b*c - a*d)^3*e*(1 + m))} 

# Integrands of the form (e x)^m (a+b x^n)^p (c+d x^n)^q (A+B x^n) with p symbolic
[(e*x)^m*(a+b*x^n)^p*(A+B*x^n)*(c+d*x^n)^q,x,7,A*(e*x)^(1+m)*(a+b*x^n)^p*(c+d*x^n)^q*AppellF1((1+m)/n,-p,-q,(1+m+n)/n,-b*x^n/a,-d*x^n/c)/(e*(1+m)*(1+b*x^n/a)^p*(1+d*x^n/c)^q)+B*x^(1+n)*(e*x)^m*(a+b*x^n)^p*(c+d*x^n)^q*AppellF1((1+m+n)/n,-p,-q,(1+m+2*n)/n,-b*x^n/a,-d*x^n/c)/((1+m+n)*(1+b*x^n/a)^p*(1+d*x^n/c)^q)],

#  {(e*x)^m*(a + b*x^n)^p*(c + d*x^n)^3*(A + B*x^n), x, 11, (A*c^3*(e*x)^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(e*(1 + m))) + (c^2*(B*c + 3*A*d)*x^(1 + n)*(e*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + n)/n, -p, (1 + m + 2*n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(1 + m + n)) + (3*c*d*(B*c + A*d)*x^(1 + 2*n)*(e*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + 2*n)/n, -p, (1 + m + 3*n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(1 + m + 2*n)) + (d^2*(3*B*c + A*d)*x^(1 + 3*n)*(e*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + 3*n)/n, -p, (1 + m + 4*n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(1 + m + 3*n)) + (B*d^3*x^(1 + 4*n)*(e*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + 4*n)/n, -p, (1 + m + 5*n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(1 + m + 4*n))} 

#  {(e*x)^m*(a + b*x^n)^p*(c + d*x^n)^2*(A + B*x^n), x, 9, (A*c^2*(e*x)^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(e*(1 + m))) + (c*(B*c + 2*A*d)*x^(1 + n)*(e*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + n)/n, -p, (1 + m + 2*n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(1 + m + n)) + (d*(2*B*c + A*d)*x^(1 + 2*n)*(e*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + 2*n)/n, -p, (1 + m + 3*n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(1 + m + 2*n)) + (B*d^2*x^(1 + 3*n)*(e*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + 3*n)/n, -p, (1 + m + 4*n)/n, -((b*x^n)/a)])/((1 + (b*x^n)/a)^p*(1 + m + 3*n))} 
[(e*x)^m*(a+b*x^n)^p*(A+B*x^n)*(c+d*x^n),x,4,-(a*B*d*(1+m+n)-b*(A*d*n+B*c*(1+m+n*(2+p))))*(e*x)^(1+m)*(a+b*x^n)^(1+p)/(b^2*e*(1+m+n+n*p)*(1+m+n*(2+p)))+d*(e*x)^(1+m)*(a+b*x^n)^(1+p)*(A+B*x^n)/(b*e*(1+m+n*(2+p)))-(A*b*(1+m+n+n*p)*(a*d*(1+m)-b*c*(1+m+n*(2+p)))-a*(1+m)*(a*B*d*(1+m+n)-b*(A*d*n+B*c*(1+m+n*(2+p)))))*(e*x)^(1+m)*(a+b*x^n)^p*hypergeom([(1+m)/n,-p],[(1+m+n)/n],-b*x^n/a)/(b^2*e*(1+m)*(1+m+n+n*p)*(1+m+n*(2+p))*(1+b*x^n/a)^p)],
[(e*x)^m*(a+b*x^n)^p*(A+B*x^n)/(c+d*x^n),x,6,-(B*c-A*d)*(e*x)^(1+m)*(a+b*x^n)^p*AppellF1((1+m)/n,-p,1,(1+m+n)/n,-b*x^n/a,-d*x^n/c)/(c*d*e*(1+m)*(1+b*x^n/a)^p)+B*(e*x)^(1+m)*(a+b*x^n)^p*hypergeom([(1+m)/n,-p],[(1+m+n)/n],-b*x^n/a)/(d*e*(1+m)*(1+b*x^n/a)^p)],
[(e*x)^m*(a+b*x^n)^p*(A+B*x^n)/(c+d*x^n)^2,x,7,(B*c-A*d)*(e*x)^(1+m)*(a+b*x^n)^(1+p)/(c*(b*c-a*d)*e*n*(c+d*x^n))-(a*d*(B*c*(1+m)-A*d*(1+m-n))+b*c*(A*d*(1+m-n*(1-p))-B*c*(1+m+n*p)))*(e*x)^(1+m)*(a+b*x^n)^p*AppellF1((1+m)/n,-p,1,(1+m+n)/n,-b*x^n/a,-d*x^n/c)/(c^2*d*(b*c-a*d)*e*(1+m)*n*(1+b*x^n/a)^p)-b*(B*c-A*d)*(1+m+n*p)*(e*x)^(1+m)*(a+b*x^n)^p*hypergeom([(1+m)/n,-p],[(1+m+n)/n],-b*x^n/a)/(c*d*(b*c-a*d)*e*(1+m)*n*(1+b*x^n/a)^p)],

#  {(e*x)^m*(a + b*x^n)^p*(A + B*x^n)/(c + d*x^n)^3, x, 4, (B*(e*x)^(1 + m)*(a + b*x^n)^p*(1 + (d*x^n)/c)^2*AppellF1[(1 + m)/n, -p, 2, (1 + m + n)/n, -((b*x^n)/a), -((d*x^n)/c)])/((1 + (b*x^n)/a)^p*(d*e*(1 + m)*(c + d*x^n)^2)) - ((B*c - A*d)*(e*x)^(1 + m)*(a + b*x^n)^p*(1 + (d*x^n)/c)^3*AppellF1[(1 + m)/n, -p, 3, (1 + m + n)/n, -((b*x^n)/a), -((d*x^n)/c)])/((1 + (b*x^n)/a)^p*(d*e*(1 + m)*(c + d*x^n)^3))} 

# Integrands of the form (g x)^m (a+b x^(n/2)^p (c+d x^(n/2))^p (e+f x^n)^r with b c+a d=0

# Integrands of the form x^m (a+b x^(n/2)^p (c+d x^(n/2))^p (e+f x^n)^r with b c+a d=0
[(-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,4,(c/a^2+d/b^2)*(-a+b*x^(1/2*n))^(1/n)*(a+b*x^(1/2*n))^(1/n)/x-d*(-a+b*x^(1/2*n))^(1/n)*(a+b*x^(1/2*n))^(1/n)*hypergeom([(-1)/n,(-1)/n],[(-1+n)/n],b^2*x^n/a^2)/(b^2*x*(1-b^2*x^n/a^2)^(1/n))],
[(-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,4,(c/a^2+d/b^2)*(-a+b*x^(1/2*n))^(1/n)*(a+b*x^(1/2*n))^(1/n)/x-d*(-a+b*x^(1/2*n))^(1/n)*(a+b*x^(1/2*n))^(1/n)*hypergeom([(-1)/n,(-1)/n],[(-1+n)/n],b^2*x^n/a^2)/(b^2*x*(1-b^2*x^n/a^2)^(1/n)),-(c/a^2+d/b^2)*(-a+b*x^(1/2*n))^(-1+1/n)*(a+b*x^(1/2*n))^(-1+1/n)*(a^2-b^2*x^n)/x+a^2*d*(-a+b*x^(1/2*n))^(-1+1/n)*(a+b*x^(1/2*n))^(-1+1/n)*hypergeom([(-1)/n,(-1)/n],[(-1+n)/n],b^2*x^n/a^2)/(b^2*x*(1-b^2*x^n/a^2)^((1-n)/n))]]:
