Question

Find :
$\int xcosxdx$.

Answer 1

Let $u=x\Rightarrow du=dx$ and $dv=\cos xdx\Rightarrow v=\sin x$

Integrating by parts, we get

$\int u.dv=uv-\int v.du$

$=x\sin x-\int \sin xdx$

$=x\sin x-(-\cos x)+c$

$=x\sin x+\cos x+c$ where $c$ is the integration constant.