Prove that: $\displaystyle \int_0^{\infty}x^n e^{-x} dx=n!;\ n=0,1,2...$
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Originally Posted by acevipa Prove that: $\displaystyle \int_0^{\infty}x^n e^{-x} dx=n!;\ n=0,1,2...$ Hint: Spoiler: Induction and integration by parts
'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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