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Challenging integral with exponential functions

  1. Jul 22, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm unable to integrate the following function with respect to x [-inf, +inf]:

    2. Relevant equations


    3. The attempt at a solution

    I tried to expand the function by distributing the exponent (-n) across the rightmost product, but I don't think its possible. Does a clever substitution method exist?
    Last edited: Jul 22, 2009
  2. jcsd
  3. Jul 22, 2009 #2
    Indefinite integral?
  4. Jul 22, 2009 #3


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    Staff Emeritus
    Science Advisor
    Gold Member

    You can try some sort of induction argument. Integration by parts: eyx and dx/(1+ex)n probably gives you something based on the integral of [tex]\frac{e^{yx}}{(1+e^x)^{n-1}}[/tex]
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