# Deriving the rms speed from the Maxwell speed distribution

## Homework Statement

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.

## 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.

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