This is integration by parts.
\(\int f(x)=\int x \cos x d x\)
\(let \(n=x: \frac{d u}{d x}=1 \Rightarrow d u=d\)
let \(d=\cos x d=\cos x d x\)
\(v=\int \cos x d x=\sin x\)
Using integration by part technique. i.e.
\begin{aligned}
&\int u d v=w-\int v d u \\
&\int x \cos x=x \sin x-\int \sin x d x \\
&=x \sin x-(-\cos x)+k \\
&=x \sin x+\cos x+k
\end{aligned}