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Integration by parts

  1. Jun 11, 2009 #1
    1. The problem statement, all variables and given/known data

    I have attempted and failed solving the following integration:

    Integrate : e^(-x) cos x dx
    2. Relevant equations
    I tried using the integration by parts rule:

    uv - (integral) v (du/dx) dx

    3. The attempt at a solution

    I let u = e^(-x) and dv/dx = cos x

    therefore (du/dx) = -e^(-x) and v = sin x

    e^(-x)sinx - (integral)-e^(-x)sinx dx

    This does not seem to cancel out anything and just keeps cycling through e and sin/cos
     
  2. jcsd
  3. Jun 11, 2009 #2

    diazona

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    Integrate by parts twice, and you will come up with an equation you can solve for the integral you want.
     
  4. Jun 11, 2009 #3

    Cyosis

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    Alternatively you could write the integral as [itex]\text{Re}(\int e^{-x}e^{i x} dx )[/itex].
     
  5. Jun 11, 2009 #4
    I just end up with having to integrate exactly what I began with!

    After doing parts twice i get

    -e-xcosx - [tex]\int[/tex] e-x cosx dx
     
  6. Jun 11, 2009 #5

    Cyosis

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    Where did the first term, e^(-x)sinx, from the first partial integration go? Now define [itex]I=\int e^{-x}\cos x dx[/itex]. You will then get an equation I= (some stuff)-I, we want to know I therefore solve for I!
     
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