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Integral with exponential terms?

  1. May 3, 2014 #1
    I am doing some analysis and I have come up with the following integral:

    [itex]\int \frac{e^{-ax}}{1+be^{-cx}}dx[/itex]

    where [itex]a>0[/itex], [itex]b>0[/itex] and [itex]c>0[/itex].

    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
     
  2. jcsd
  3. May 3, 2014 #2

    lurflurf

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    Homework Helper

    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.
     
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