How do you integrate $y = x e^{- x}$ $y=xe^(-x)$ ?

Question

82471 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-04T13:25:33

$= - e^{- x} (x + 1) + C$ $= -e^{-x} (x +1) + C$

$int dx qquad x e^{-x}$

IBP: $int u v' = uv - int u'v$

here

$u = x, u' = 1$
$v' = e^{-x}, v = - e^{-x}$

so

$-x e^{-x} - int dx qquad (-e^{-x})$

$= -x e^{-x} - (e^{-x}) + C$

$= -e^{-x} (x +1) + C$

How do you integrate y=xe^(-x)y=xe−xy=xe^(-x)?