find-integrate-x-2-e-x-dx-

Question Number 172011 by Mikenice last updated on 23/Jun/22

f i n d i n t e g r a t e :

\int x^{2} e^{x} d x

Answered by puissant last updated on 23/Jun/22

P = \int x^{2} e^{x} d x

{\begin{cases} u^{'} = e^{x} \\ v = x^{2} \end{cases} \Rightarrow {\begin{cases} u = e^{x} \\ v^{'} = 2 x \end{cases}

P = x^{2} e^{x} - 2 \int {x e}^{x} d x

P = x^{2} e^{x} - 2 {x e}^{x} + 2 e^{x} + C

P = (x^{2} - 2 x + 2) e^{x} + C

Facebook Tweet Pin