Hello, Forum! I just registered after seeing you actually help people understand their problems. That's great. We have (or should have) learned about linearity, substitution and partial integration. However, I don't know when to use which! Could someone also give me a bit of an expanation on this? :( I have to solve an integral: x*e^(-3x) dx My train of thought: I have almost got 2 'basis integrals': x dx and e^x dx. I probably need to substitute to get them to the basic form. But how! As you see I'm pretty clueless, but what I came up with was: u = -3x --> u'= -3 v' = x --> v = (x²)/2 However, this leads nowhere. I don't know what to do! According to derive, the solution is supposed to be: Code (Text): 1 -3x ⎛ x 1 ⎞ ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ - e ⎜⎯⎯⎯⎯⎯⎯⎯⎯⎯ + ⎯⎯⎯⎯⎯⎯ ⎟ 2 ⎜ 3·LN(e) 2⎟ 9·LN(e) ⎝ 9·LN(e) ⎠ I sincerely hope someone will be able to show me the light! Thanks in advance. PS: Our teacher is really bad at teaching!