Question

Find ∫ 𝑥𝑐𝑜𝑠 𝑥𝑑x

Answer 1

Solution.

$$\int x \cos xdx$$

To calculate this integral we use the method of integration by parts.

Let be $u=x, dv=\cos {x} dx.$

From here $du=1, v=\sin x.$

Therefore, $\int x\cos xdx=x\sin x-\int 1\cdot\sin xdx=x\sin x+\cos x+C,$

where $C$ is some constant.

Answer.

$$\int x\cos xdx=x\sin x+\cos x+C.$$