Antiderivative: natural logs, exponents

[swooshfactory]

Homework Statement

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

Homework Equations

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.

 

[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.