Answer
$x^2 \sin x +2x \cos x -2 \sin x +C$
Work Step by Step
Our aim is to solve the integral $ \int x^2 \cos x \ dx$
Use integration by parts formula.
$\int x^2 \cos x \ dx=x^2 \times \sin x -\int (\sin x) (2x) \ dx $
or, $=x^2 \sin x -[-2x \cos x +2 \int \cos x \ dx]$
or, $=x^2 \sin x +2x \cos x -2 \sin x +C$
