[SadBloke]

"Perform the following calculation in spherical coordinates. The Maxwell-Boltzman velocity distribution function has the form:

f(u)=(mβ/2Π)^3/2e^-mβu2/2 where β is a constant. Using the fact that ε = (mu²)/2 = (3/2)k_BT = int(du_x)int(du_y)int(du_z)((mu²)/2)f(u) and using also the definition u²=u_x²+u_y²+u_z² complete the integral and show that β=1/(k_BT)

I'll link to my instructor's lecture notes, which I didn't find especially helpful but would give you a sense of what path I'm trying to follow.
http://faculty.washington.edu/gdrobny/Lecture453_1-14_Intro.pdf

I'm currently at page 5, figure 1.14.

I was thinking that the integral in figure 1.14 may be solvable using a generic form but haven't found one that I can fit the equation to.
Any help or insight would be greatly appreciated, as I've been trying to figure it out all weekend and made zero progress.

[Corribus]

There's an integral here I believe that fits.

http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions

(Eighth one under definite integrals).

In the future, please try to use LaTex when writing equations like that. It's easy to misinterpret them the way you have them written.