Euler’s integral formula

This formula is well known n! = \int_0^{+\infty} x^n e^{-x}dx and is given as an exercise for integration by parts. Here is a nice alternative proof I came across due to Inna Zakharevich.
\int_0^{+\infty} e^{-\alpha x} dx = \frac{1}{\alpha}. Now differentiate n times wrt to \alpha and set \alpha = 1.

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