Question

$\int x{e}^{x}dx$

Answer 1

$$\begin{gathered} \int x{e}^{x}dx \\ \mathrm{Taking}x\mathrm{as}\mathrm{the}\mathrm{first}\mathrm{function}\mathrm{and}{e}^x\mathrm{as}\mathrm{the}\mathrm{second}\mathrm{function}. \\ =x\int e^{x}dx-\int \left\{\frac{d}{dx}\left(x\right)\int e^{x}dx\right\}dx \\ =x{e}^x-\int 1\left(e^x\right)dx \\ =x{e}^x-e^x+C \\ =\left(x-1\right)e^x+C \end{gathered}$$