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Integration by parts

  1. Feb 26, 2006 #1
    I'm kind of lost on where to go next with this integration by parts problem.

    I have to integrate e^xcos(x)dx.

    I've gotten as far as one step of integration by parts, but I can't understand how this will help. It seems I'll just be going in circles. I have:

    e^xsin(x) - int(e^xsin(x))dx. If I do a second integration by parts, will I not just get back to where I started?
  2. jcsd
  3. Feb 26, 2006 #2
    do parts twice, combine like terms and you can solve in terms of the original integral in question.
  4. Feb 26, 2006 #3


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    In other words, you do know how to solve z = a - z for z.

    (P.S. doesn't your textbook do this as an example?)
  5. Feb 27, 2006 #4


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    One thing that can prevents you from getting an obvious equation like 0 = 0 is that: If you previously assigned u = ex, and dv = cos(x) => v = sin(x), and get to:
    [tex]\int e ^ x \cos x dx = e ^ x \sin x - \int e ^ x \sin x dx[/tex]
    Then what you should do next is to let u = ex, and dv = sin(x).
    After that, just do some little rearrangement, and you'll arrive at the answer.
    Do NOT do the reverse (i.e, let u = sin(x), and dv = ex). If you want to see why, then just try it. Don't be surprise if you get an equation 0 = 0, or [tex]\int 0 dx = C[/tex].
    Can you go from here? :)
    Last edited: Feb 27, 2006
  6. Feb 27, 2006 #5
    that's the trick! get back where you started, and combine like terms, as in ac + bc = (a+b)c. that's the only trick to this problem.
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