integration of (x^a/(b+x))) or
integration of ((x/(b+x^a));
integration of (exp(x)/(b+exp(a*x));
integration of (exp(a*x)/(b+exp(x));
where, a and b are constants. x is variable. please find the solution for any one of the question.
No products are associated with this question.
The first one is
-x^a*(-1+LerchPhi(-x/b, 1, a)*a)/a
unless b = 0, and then it is (x^a)/a
The second one is
(1/2)*x^2*hypergeom([1, 2/a], [1+2/a], x^a*(-1)^csgn(I*x^a)/b)/b
if b < 0, and is
if b = 0, and is
(1/2)*x^2*hypergeom([1, 2/a], [1+2/a], -x^a/b)/b
if b > 0