1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    -Sparky
     
    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Integration by parts
  1. Integration by parts (Replies: 6)

  2. Integration by parts (Replies: 8)

  3. Integration by Parts (Replies: 8)

Loading...