Consider the indefinite integral 4e4x(e4x+3)5 dx\displaystyle \int\frac{{-{4}{e}^{{-{4}{x}}}}}{{\left({e}^{{-{4}{x}}}+{3}\right)}^{{5}}}\ {\left.{d}{x}\right.}:

This can be transformed into a basic integral by letting

u=\displaystyle {u}=   and

du=\displaystyle {d}{u}=dx\displaystyle {\left.{d}{x}\right.}  

Performing the substitution yields the integral

\displaystyle \intdu\displaystyle {d}{u}