Deriving the rms speed from the Maxwell speed distribution

[Tabiri]

Homework Statement

Find v_rms 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.

Homework Equations

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

Where $a$ and $x$ are constants.

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.

 

[Tabiri]

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