Difficult integration: e^u(x^2)

[Kruger]

Homework Statement

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

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.

 

[Avodyne]

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.)

 

[sprint]

maybe somehow incorporate the chain rule?