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Antiderivative: natural logs, exponents

  1. Sep 2, 2008 #1
    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. jcsd
  3. Sep 2, 2008 #2

    rock.freak667

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    Homework Helper

    [tex](3t+2e^t)e^{\frac{-3t}{2}}=3te^{\frac{-3t}{2}}+2e^{t+\frac{-3t}{2}}[/tex]


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