# Deriving the rms speed from the Maxwell speed distribution

1. Nov 20, 2013

### Tabiri

1. The problem statement, all variables and given/known data

Find vrms from the Maxwell speed distribution.

Basically what I need to solve is the integral $a\int_0^∞ \! v^4e^{xv^2} \, \mathrm{d}v$

Where $a$ and $x$ are constants.

2. Relevant equations

$$a\int_0^∞ \! v^4e^{xv^2} \, \mathrm{d}v$$

Where $a$ and $x$ are constants.

3. The attempt at a solution

I've tried u-substitution, subbing in u for $v^2$ and for $v^{2.5}$ but they end up not working.

Last edited: Nov 20, 2013
2. Nov 20, 2013

### Tabiri

Nevermind, figured it out (integrate by parts a couple times).