- #1

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- 27

## Homework Statement

If you know

[tex]\int_{-\infty}^{\infty} e^{-\alpha \beta^2} d \beta = \sqrt{\pi / \alpha} [/tex]

Show that

[tex]\int_{-\infty}^{\infty} \beta^2 e^{-\beta^2} d \beta = \sqrt{\pi}/2 [/tex]

## The Attempt at a Solution

I have tried integration by parts on the second integral, but to no avail. I just end up with it being equal to zero. What am I to do?