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Ugh integration

  1. Sep 9, 2008 #1
    How do I integrate (e^ax)sin(bx)
  2. jcsd
  3. Sep 10, 2008 #2


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    Gold Member

    I think integration by parts will work.
  4. Sep 10, 2008 #3


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    Science Advisor

    A somewhat clumsy, but direct, method is to use the representation of sin(bx) in terms of exp. Specifically:

    sin(bx)=(e^ibx - e^-ibx)/2i

    This gives you two integrals of the exp function. You can then do a little playing around to get rid of the i terms.
  5. Sep 10, 2008 #4
    Integration by parts will work, but there's a bit more to it. You will need to apply integration by parts twice. After the second application, a multiple of your original integral will reappear. You would then have to isolate this integral. In other words, you will obtain something like:

    I = (stuff from using integration by parts twice) + a*I

    where 'I' represents your original integral and 'a' is some constant. You'd then have to "solve" for the 'I'

    I just thought I'd add this because oftentimes students only apply integration by parts once and do not see the solution right away, and get flustered.
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