Question

Find :
$\int xsinxdx$.

Answer 1

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

Integrating by parts, we get

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

$=-x\cos x-\int -\cos xdx$

$=-x\cos x+\int \cos xdx$

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