Question

Integerate:
$\int x\cos xdx$

Answer 1

Consider the given integral.

$I=\int x\cos xdx$

We know that

$\int uvdx=u\int vdx-\int (\frac{d}{dx}\left(u\right)\int vdx)dx$

Therefore,

$I=x\sin x-\int 1\times \left(\sin x\right)dx$

$I=x\sin x-\int \left(\sin x\right)dx$

$I=x\sin x-(-\cos x)+C$

$I=x\sin x+\cos x+C$

Hence, this is the answer