find integrate: ∫xe^x dx


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Question Number 172010 by Mikenice last updated on 23/Jun/22

$f i n d i n t e g r a t e :$ $\int {x e}^{x} d x$
	Answered by puissant last updated on 23/Jun/22
	$K=∫xe^x dx ; { ((u′=e^x )),((v=x)) :}⇒ { ((u=e^x )),((v′=1)) :} ⇒ K=[xe^x ]−∫e^x dx ⇒ K=e^x (x−1)+C$
	$K = \int {x e}^{x} d x; {\begin{cases} u^{'} = e^{x} \\ v = x \end{cases} \Rightarrow {\begin{cases} u = e^{x} \\ v^{'} = 1 \end{cases}$ $\Rightarrow K = [{x e}^{x}] - \int e^{x} d x$ $\Rightarrow K = e^{x} (x - 1) + C$
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