Integral with exponential terms?

[fchopin]

I am doing some analysis and I have come up with the following integral:

$\int \frac{e^{-ax}}{1+be^{-cx}}dx$

where $a>0$, $b>0$ and $c>0$.

I have found out this integral has a solution in terms of the Gaussian hypergeometric function http://en.wikipedia.org/wiki/Hypergeometric_function but it looks to me that it should have a solution in terms of simple mathematical functions.

Is there any solution to this integral in terms of simple functions?

Thanks in advance

 

[lurflurf]

The hypergeometric function is a simple mathematical function. You could also use the beta function or an infinite series. Those three forms are closely related and none is really any more simple than another.