# How do you integrate x^2 e^-x?

$\int {x}^{2} \cdot {e}^{-} x \mathrm{dx} = - {e}^{-} x \cdot {x}^{2} + \int {e}^{-} x 2 x \mathrm{dx} = - {x}^{2} \cdot {e}^{-} x - 2 x \cdot {e}^{-} x + 2 \cdot \int {e}^{-} x \mathrm{dx} = - {e}^{-} x \cdot \left({x}^{2} + 2 x + 2\right) + c$
$\int f ' \left(x\right) \cdot g \left(x\right) \mathrm{dx} = f \left(x\right) \cdot g \left(x\right) - \int f \left(x\right) \cdot g ' \left(x\right) \mathrm{dx}$