Question

Integrate the function.
$\int xsinxdx.$

Answer 1

Let $I=\int sinx.xdx$
On taking x as first function and sin x as second function and integrating by parts, we get
$I=x\int sinxdx-\int \left[\frac{d}{dx}\right(x)\int sinxdx]dx$
$=-xcosx+\int 1.cosxdx$
$\Rightarrow I=-xcosx+sinx+C$