Question

Anyone know how to evaluate Gaussian Integrals?

Answer 1

In the case we're integrating over the entire real line, or half the real line, it's fairly straight-forward, see here:
http://en.wikipedia.org/wiki/Gaussian_integral

But in the case you're integrating to or from some finite point, you have to use numerical methods.

Answer 2

What kind of Math are you in?

Answer 3

I am more interested in more difficult integrals of that sort such as:
\[\int\limits_{-\infty}^{\infty} dx \frac{x^n}{e^x-1}\]
Or something similar. I know there are analytic ways to solve them and I've learned analytic ways to solve ones of the following form:
\[\int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty} ... \int\limits_{-\infty}^{\infty} dx_1dx_2...dx_n \exp[\alpha x_1^nx_2^n...x_n^n+\beta x^1_{n-1}...]\]