Prove that:

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

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- Jun 7th 2010, 06:41 PMacevipaProving improper integral equals n!
Prove that:

$\displaystyle \int_0^{\infty}x^n e^{-x} dx=n!;\ n=0,1,2...$ - Jun 7th 2010, 06:43 PMDrexel28
- Jun 7th 2010, 06:44 PMmaddas
'ullo Laplace transform.

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

edit: too slow!