IMathAS-libretexts

Consider the indefinite integral

\displaystyle \int\frac{{x}^{{5}}}{{\left({x}^{{6}}+{7}\right)}^{{6}}}\ {\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}