# Homework Help: Antiderivative: natural logs, exponents

1. Sep 2, 2008

### swooshfactory

1. The problem statement, all variables and given/known data

I am trying to anti-differentiate (3t+2e^t)*[e^(-3t/2)]

2. Relevant equations

3. The attempt at a solution

I have simplified this into several forms, including [3t(e^(-3t/2)+2e^(-t/2)] . This form may or may not be accurate, but I am pretty sure that the form given at the beginning of this post is accurate. But I cannot anti-differentiate either of them. A u-substitution maybe? I'm not sure. I cannot move past the problem I need to solve until I complete this step. Any help would be appreciated. Thank you for looking.

2. Sep 2, 2008

### rock.freak667

$$(3t+2e^t)e^{\frac{-3t}{2}}=3te^{\frac{-3t}{2}}+2e^{t+\frac{-3t}{2}}$$

Simplify this $t+\frac{-3t}{2}$ part. Then use integration by parts on the $te^{\frac{-3t}{2}}$ term.