Solution
= Solution
For <integration by parts>, take $u=x$ and $dv=\cos x\,dx$. Then $du=dx$ and $v=\sin x$, giving the <antiderivative>
$$
\boxed{\int x\cos x\,dx=x\sin x+\cos x+C.}
$$
= Solution
For <integration by parts>, take $u=x$ and $dv=\cos x\,dx$. Then $du=dx$ and $v=\sin x$, giving the <antiderivative>
$$
\boxed{\int x\cos x\,dx=x\sin x+\cos x+C.}
$$