Question

$\int x^2\cos xdx$

Answer 1

$$\begin{gathered} \int x^2\cos xdx \\ \mathrm{Taking}{x}^2\mathrm{as}\mathrm{the}\mathrm{first}\mathrm{function}\mathrm{and}\cos x\mathrm{as}\mathrm{the}\mathrm{second}\mathrm{function}. \\ =x^2\int \cos xdx-\int \left(\frac{d}{dx}{x}^2\int \cos xdx\right)dx \\ =x^2\sin x-\int 2x\sin xdx \\ =x^2\sin x-2\left[x\int \sin x-\int \left\{\frac{d}{dx}\left(x\right)\int \sin xdx\right\}dx\right] \\ =x^2\sin x-2\left[-x\cos x+\int \cos xdx\right] \\ =x^2\sin x+2x\cos x-2\sin x+C \end{gathered}$$