MGF for the Rayleigh distribution

Hi, I'm trying to derive the moment generating function for the Rayleigh distribution.

I know that it equals E(e^(t*x)), which is the following integral that can be seen here, evaluated at the limits of 0 and infinity:

http://www.wolframalpha.com/input/?i...9%29%29%2Cx%5D

Where the parameter is σ.

However, I'm having trouble in the actual derivation of this. I've been trying to do a change of variable where u = -(x^2/(2*(sigma^2))), so that I can get the integral to appear somewhere for the error function, but I'm not making any progress. Can someone help me in moving this along? Thanks.

There doesn't seem to be a closed form for this MGF
Rayleigh distribution - Wikipedia, the free encyclopedia
I'm not sure what you need help with.
Show me the calculations