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Homework Help: Integration by parts

  1. Jan 6, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex] \int e^{2x}sin(e^x)dx [/tex]

    2. Relevant equations

    Can I make the substitution:

    [tex] w = e^x ; dw = e^x dx [/tex]

    Making a "new / simpler" problem:

    [tex] \int w sin(w) [/tex]

    3. The attempt at a solution

    Using integration by parts on the "new" problem:

    [tex] u = w ; dw = du [/tex]
    [tex] dv = sin (w) ; v = -cos(w)[/tex]

    [tex] \int w sin(w) dw = -w cos(w) +\int cos(w) dw [/tex]

    [tex]= -w cos(w) + sin(w)[/tex]

    [tex]= -e^xcos(e^x) + sin(e^x) [/tex]

    is this correct?

    This integral is part of a larger problem and this term should "go away" supposedly.

    If this is correct (this solution does not simplify to 0), then I will need to post the larger problem -
    Thanks for the help
    Last edited: Jan 6, 2008
  2. jcsd
  3. Jan 6, 2008 #2
    Your problem isn't really that clear to me, is this correct ...

    [tex]\int e^{2x}\sin(e^x)dx[/tex]
  4. Jan 6, 2008 #3
    Yes - sorry I was still making my problem presentable when you replied.

    It's impressive how quickly you replied.
  5. Jan 6, 2008 #4

    Your initial sub. is perfect so no problem there.

    I also get your final answer except with +C at the end which should always be included with indefinite integrals.
    Last edited: Jan 6, 2008
  6. Jan 6, 2008 #5
    Well it checks out and is correct. If you want to know if your Integration is correct, just take the derivative of your answer.
  7. Jan 6, 2008 #6
    Sometime soon, I'll try to post the entire problem - it's a differential equation from a book.

    I'm not in school but I am trying to brush back up. I have the answer to it - 3 terms summed. I have 4 terms - 3 agree with the 3 - I have an extra.

    I'll try to post it perhaps tomorrow. - It's on about 5-6 pages of paper.

    I'll condense as appropriate.

    thanks for the help.
  8. Jan 6, 2008 #7
    Gotcha, I'm subscribed.
    Last edited: Jan 6, 2008
  9. Jan 7, 2008 #8
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