# Integral from 0 to Infinity

Show that the

integral from 0 to infinity of (t^n e^-t dt) = n!

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#### Solution Preview

By parts,

I = integral(0 to inf)[t^n e^-t dt]

= {-t^n e^(-t)}(U=inf, L=0) + n*integration(0 to inf)[t^(n-1) e^(-t) dt]

Here, U = upper limit = ...

#### Solution Summary

This is how to show a given integral is a factorial.

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