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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.

*No products are associated with this question.*

Answer by Walter Roberson on 26 Sep 2012

Accepted answer

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!

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