Consider the integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{-x}dx$ :

Applying the integration by parts technique, let

$u=$ and $du=,dx$

$dv=,dx$ and $v=$

Then $uv-{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$vdu$=$

$-{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}},dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{-x}dx=$