# Math Help - Proving improper integral equals n!

1. ## Proving improper integral equals n!

Prove that:

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

2. Originally Posted by acevipa
Prove that:

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

Spoiler:
Induction and integration by parts

3. 'ullo Laplace transform.

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

edit: too slow!