# Integral of Maxwell-Boltzmann dist.

1. Apr 18, 2013

### Denver Dang

1. The problem statement, all variables and given/known data
I was wondering if there is some sort of trick to calculate the following:
$$\int{-{{e}^{-\varepsilon /{{k}_{B}}T}}}{{\varepsilon }^{3/2}}d\varepsilon \,$$
It's the derivative of the Maxwell-Boltzmann distribution, excluding the constants, times an energy in the power of (3/2).

2. Relevant equations

3. The attempt at a solution
I've found the solution from 0 to infinity if the energy was powered in n (n being an integer), but I haven't been able to find anything when it's a half-integer.

So is there some sort of trick to do this, or...?

2. Apr 18, 2013

### Dick

Since integer powers are nicer why not substitute $\epsilon=u^2$? Now you've got a gaussian times an integer power of u. That's a pretty well known problem.

3. Apr 18, 2013

### Denver Dang

Ahhh yes, that should work. Don't know why I didn't think of that :/

Thank you :)