Integrate by parts: .
Here you set and so and .
Hence, as they say, the result.
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?