Question

solve it.
$I=\int x^2\cos xdx$

Answer 1

$I=\int x^2\cos xdx$

Let $u=x^2\Rightarrow du=2xdx$

$dv=\cos xdx\Rightarrow v=\sin x$

$I=x^2\sin x-\int 2x\sin xdx$

$I=x^2\sin x-2\int x\sin xdx$

Let $u=x\Rightarrow du=dx$

$dv=\sin xdx\Rightarrow v=-\cos x$

$I=x^2\sin x-2[-x\cos x+\int \cos xdx]$

$I=x^2\sin x+2x\cos x-2\int \cos xdx$

$I=x^2\sin x+2x\cos x-2\sin x+c$