Answer
$-x^2 \cos x+2x \sin x+2 \cos x+C$
Work Step by Step
Our aim is to solve the integral $ \int x^{2} \sin x \ dx$
Let us consider that $a =x^{2}$ and $\ da=2 x dx$ and $db =\sin x dx$ and $b=-\cos x$
Now, $ \int x^{2} \sin x \ dx=-x^2 \cos x+\int 2x \cos x \ dx$
or, $= -x^2 \cos x+[2x \sin x-2 \int \sin x dx]$
or, $= -x^2 \cos x+2x \sin x-2 \int \sin x \ dx$
or, $= -x^2 \cos x+2x \sin x+2 \cos x+C$
