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Difficult integration: e^u(x^2)

  1. Nov 8, 2007 #1
    1. The problem statement, all variables and given/known data

    Given the function g(x)=e^u(x) where u(x) = -(1-x^2)^(-1). I have to integrate this from -1 to 1.

    3. The attempt at a solution

    I know the function is symmetric. It is enough to integrate it from 0 to 1 to get the real value of the integral. Well, beside that I have absolutely no clue how to do that. I need this in order to construct out of it a Dirac function. But my first task, as the homework states, is to solve this integral. (I tried to substitute something (but failed) and after that I wanted to use the Cauchy Integral Formule (extend the function to complex plane), but this didn't work either (because I couldn't get it in a appropriate form, as for the CIF needed)).

    So I would be very pleased if someone can give me a hint. Perhaps a little bit more than a hint.
  2. jcsd
  3. Nov 8, 2007 #2


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    I don't think there is a way to do it. Neither does Mathematica. (Well, it gives an answer in terms of Meijer G functions, but that seems excessive.)
  4. Nov 8, 2007 #3
    maybe somehow incorporate the chain rule?
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