Consider the indefinite integral ∫x5+6x45 dx\displaystyle \int\frac{{{\sqrt[{{5}}]{{{x}}}}+{6}}}{{{\sqrt[{{5}}]{{{x}^{{{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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