Question

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

Answer 1

$I=\int \underset{I}{x}\underset{II}{e^x}dx$

Applying integration by parts,

$I=x\int e^{x}dx-{\int }_{dx}dx\int e^{x}dx$

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

$=x{e}^x-e^x+c$.