Consider the integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(7x+8)cos(5x)dx$ :

Applying the integration by parts technique, let

$u=$ and $du=|,dx||$

$dv=,dx$ and $v=$

Then the integration by parts formula yields

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

so that

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(7x+8)cos(5x)dx=,+C$