Math Help - Improper integral question

1. Improper integral question

The question:
$\int_{-\infty}^{\infty} x^3e^{-x^4} dx$

I tried integration by parts, but it quickly became a long mess. :/

How should one attempt this question? Thanks!

2. Let $u = -x^4$, then: $dx = -\frac{du}{4x^3}$

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That's the antiderivative -- now do your thing with the limits.

3. Ahh, how silly of me. Thank you!