integrate [xe^(-x)] with respect to x.

integrating a product of functions of x - integration by parts. integral of uv' = uv - integral of u'v. choice of u from LIATE - logs, inverse trig, algebra, trig, exponentials - choose u=x. u=x, v'=e^(-x). to find u', differentiate u. u' = 1. to find v, integrate v'. v = -e^(-x). we now have everything we need to integrate by parts; integral of uv' = uv - integral of u'v => integral of xe^(-x) = -xe^(-x) - integral of -e^(-x) = -xe^(-x) - e^(-x) + c = -(x+1)e^(-x) + c