Consider the integral ∫x5ln⁡(x) dx\displaystyle \int{x}^{{5}}{\ln{{\left({x}\right)}}}\ {\left.{d}{x}\right.}:

Applying the integration by parts technique, let

u=\displaystyle {u}=   and

dv=\displaystyle {d}{v}= dx\displaystyle {\left.{d}{x}\right.}  

Then uv−∫vdu\displaystyle {u}{v}-\int{v}{d}{u} =

  -∫\displaystyle \int dx\displaystyle {\left.{d}{x}\right.}  

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