Consider the indefinite integral ∫x3(x4+5)4 dx\displaystyle \int\frac{{x}^{{3}}}{{\left({x}^{{4}}+{5}\right)}^{{4}}}\ {\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}  

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