Consider the indefinite integral $\displaystyle \int{x}{\sqrt[{{3}}]{{{x}^{{2}}+{7}}}}\ {\left.{d}{x}\right.}$:

This can be transformed into a basic integral by letting

$\displaystyle {u}=$ and

$\displaystyle {d}{u}=$$\displaystyle {\left.{d}{x}\right.}$

Performing the substitution yields the integral

$\displaystyle \int$$\displaystyle {d}{u}$