I solved this problem a couple months ago, but seem to have forgotten some rules of calculus with regards to e in the meantime. The goal is to just solve this integral. Integral from 0 to +inf of (e^tx) times (5e^-5x) dx Now - in my work I got the answer of 5/5-t, which is correct. In the key that I have the answer to, one tip they give is that they use the integration rule of: Integral from 0 to +inf of e^-at dt = 1/a if a>0. So, I went at it with the standard integration by parts, but quickly realized I had forgotten some rules about multiplying e^ax X e^something else, because I couldn't terminate the integrals to get to the point of reaching 5/5-t. Just basically did something like: u= e^tx, dv= 5e^-5x -> du= te^tx, v=: -e^-5x but I think I forgot a rule somewhere as when I put it into uv - S vdu form I realized I was stuck. Does anyone know how to solve this? Do I need to do IBP a few times, or can I multiply the e's together to get to the form from before? -or- Do I not need to do IBP at all? Is the integral in its original form of Integral from 0 to +inf (e^tx) times (5e^-5x) dx able to be multiplied out to get to the e^-at form required in the answer? Looking over it now, I'm starting to figure this may be true. But like I said before, I've forgotten some rules with multiplying the two together. Any help would be appreciated. Thanks. edit - sorry for the sloppy formatting in some places, I'm unfamiliar with the codes here. I just copied the integral code from someone else's post to make it look sorta nice. The basic integral is (e^tx times 5e^-5x).