## can any one solve the Integration of following expression?

on 26 Sep 2012

### Walter Roberson (view profile)

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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### Walter Roberson (view profile)

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

### Matt Fig (view profile)

on 26 Sep 2012
Edited by Matt Fig

### Matt Fig (view profile)

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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