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

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Answer 1 · 2016-07-04T13:25:33

#= -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#