find integrate: ∫x^2 e^x dx


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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
	$P = ∫x^2 e^x dx { ((u′=e^x )),((v=x^2 )) :} ⇒ { ((u=e^x )),((v′= 2x)) :} P= x^2 e^x − 2∫xe^x dx P=x^2 e^x − 2xe^x +2e^x +C P = (x^2 −2x+2)e^x +C$
	$P = \int x^{2} e^{x} d x$ ${\begin{cases} u^{'} = e^{x} \\ v = x^{2} \end{cases} \Rightarrow {\begin{cases} u = e^{x} \\ v^{'} = 2 x \end{cases}$ $P = x^{2} e^{x} - 2 \int {x e}^{x} d x$ $P = x^{2} e^{x} - 2 {x e}^{x} + 2 e^{x} + C$ $P = (x^{2} - 2 x + 2) e^{x} + C$
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