can any one solve the Integration of following expression?

integration of (x^a/(b+x))) or

integration of ((x/(b+x^a));

or

integration of (exp(x)/(b+exp(a*x));

or

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.

Answer 1

[Walter Roberson]

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

-x^2/((a-2)*x^a)

if b = 0, and is

(1/2)*x^2*hypergeom([1, 2/a], [1+2/a], -x^a/b)/b

if b > 0

Answer 2

[Matt Fig]

Do you have the symbolic toolbox?

If not, use the online integrator from Mathematica.

Also, I think you have imbalanced parenthesis on ALL of your expressions!