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Math Help - Proving improper integral equals n!

  1. #1
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    Proving improper integral equals n!

    Prove that:

    \int_0^{\infty}x^n e^{-x} dx=n!;\ n=0,1,2...
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by acevipa View Post
    Prove that:

    \int_0^{\infty}x^n e^{-x} dx=n!;\ n=0,1,2...
    Hint:

    Spoiler:
    Induction and integration by parts
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  3. #3
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    'ullo Laplace transform.

    Use induction, reducing the n case to the n-1 case using integration by parts.

    edit: too slow!
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