Evaluate

The integral from 0 to 5 of (t)(e^-t)dt.

I got -5e^-5+-e^-5, but this is incorrect.

After integration by parts I got

-te^-t - e^-t

which from 0 to 5 gave me

-5e^-5 - e^-5 - [0 - e^0]
= -5e^-5 - e^-5 + 1