Question

$\int x\cos xdx$

Answer 1

$$\begin{gathered} \int x\cos xdx \\ \mathrm{Taking}x\mathrm{as}\mathrm{the}\mathrm{first}\mathrm{function}\mathrm{and}\cos x\mathrm{as}\mathrm{the}\mathrm{second}\mathrm{function}. \\ =x\int \cos xdx-\int \left\{\frac{d}{dx}\left(x\right)\int \cos xdx\right\}dx \\ =x\sin x-\int \sin xdx \\ =x\sin x+\cos x+C \end{gathered}$$