Answer
$\int x\sin xdx=\sin x - x\cos x + C$
Work Step by Step
Let $\frac{d}{dx}(\sin x - x\cos x)$
Using product rule:
$\frac{d}{dx}(\sin x - x\cos x)= \cos x - [x(-\sin x) +\cos x]
$
Simplify:
$\frac{d}{dx}(\sin x - x\cos x)= \cos x +x\sin x - \cos x=x\sin x$
Thus, a corresponding integration formula is
$\int x\sin x dx=\sin x - x\cos x + C$
