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How would I integrate exp(x)*cos(x)

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data

    How would I integrate exp(x)*cos(x), exp is referring to euler's number

    2. Relevant equations



    3. The attempt at a solution

    u substitution doesn't work
     
  2. jcsd
  3. Jan 21, 2010 #2

    tiny-tim

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    Hi ComFlu945! :smile:

    Integrate by parts twice, and then use a bit of ingenuity. :wink:
     
  4. Jan 21, 2010 #3

    Hurkyl

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    What would you even substitute? :eek: Well, I guess there are two or three things to try -- and you saw none of them worked out.

    What other methods do you know?
     
  5. Jan 21, 2010 #4

    benorin

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    [tex]e^x \cos x =\Re \, e^{(1+i)x}[/tex] which integrates nicely.
     
  6. Jan 21, 2010 #5

    Char. Limit

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    Isn't that a bit complex (pun?) though?

    I'd just do the integration by parts thing.
     
  7. Jan 21, 2010 #6

    tiny-tim

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    Yes, it's a nice trick, and it integrates nicely, but then you've got to simplify it, which is awkward and easy to get wrong. :redface:
     
  8. Jan 21, 2010 #7

    Hurkyl

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    Not to mention it lets you avoid this wonderful exercise that reminds us of something that is often forgotten....
     
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