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.