Answer
$- x \cos x -\sin x+C$
Work Step by Step
Our aim is to solve the integral $ \int x \sin x \ dx$
Use integration by parts formula.
$ \int x \sin x \ dx =x \times -\cos x -\int (-\cos x) \ dx $
or, $=- x \cos x +\int \cos x \ dx$
or, $=- x \cos x -\sin x+C$
