Question

Integrate:

$\int x\sin 2xdx$

Answer 1

$\int x\sin 2xdx$

Differentiating by parts

$\int x\sin 2x=x\int \sin 2xdx-\int \frac{d\left(x\right)}{dx}(\int \sin 2xdx)dx$

$=\frac{x}{2}\cos 2x-\frac{1}{2}\int \cos 2xdx=\frac{x}{2}\cos 2x+\frac{1}{4}\sin 2x+C$