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## Homework Statement

I am having trouble integrating ∫ (x = -∞ to +∞) x

^{3}e

^{-αx2}dx part--is this 0 or 1/α

^{2}? And, could someone explain? I am pretty sure that, when

∫ (x =0 to +∞) x

^{3}e

^{-αx2}dx = 1/α

^{2}

However, with x = -∞ to +∞, and the function of the equation being odd, I am lost.

## Homework Equations

above

## The Attempt at a Solution

above