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Math Help - Improper integral question

  1. #1
    Senior Member
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    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!
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  2. #2
    Super Member
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    Thanks
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    Let u = -x^4, then: dx = -\frac{du}{4x^3}

    [LaTeX ERROR: Convert failed]

    That's the antiderivative -- now do your thing with the limits.
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  3. #3
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    Ahh, how silly of me. Thank you!
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