Thread: Integrate xe^x dx

it is actually integrate from 0 to -infin, but I understand that part. When I see xe^x I integrate it and get (1/2x^2)(e^x). My solutions manuel says it is (x-1)(e^x). I don't get the same answer when using my work, what am I doing wrong?

Integrate by parts: .

Here you set and so and .

Hence, as they say, the result.

So how does (xe^x)-(e^x) become (x-1)e^x? I'm sure I'm missing some simple rule here...

Yes:

(xe^x)-(e^x)

= xe^x - e^x

= e^x(x - 1)

= (x - 1)e^x