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Integral from 0 to Infinity

Show that the

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

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.