Question

$\int x^2{e}^{x}dx$ =

Answer 1

Integrating by parts,

$u=x^2$ , $v=e^x$

$u^{{}^{\prime }}=2x$ , $\int vdx=e^x$

$⟹x^2{e}^x-\int 2x{e}^{x}dx$

Again integrating by parts,we get

$u=x$ , $v=e^x$

$u^{{}^{\prime }}=1$, $\int vdx=e^x$

$⟹x^2{e}^x-2x{e}^x+2\int e^{x}dx$

$⟹x^2{e}^x-2x{e}^x+2e^x+c$