1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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


    User Avatar
    Homework Helper

    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


    User Avatar
    Homework Helper

    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


    User Avatar
    Homework Helper

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook