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can any one solve the Integration of following expression?

Asked by Siva Malla on 26 Sep 2012

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.

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Answer by Walter Roberson on 26 Sep 2012

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 by Matt Fig on 26 Sep 2012
Edited by Matt Fig on 26 Sep 2012

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!