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Repeating integration by parts

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data

    integrate .5e^(t/50)*sin(t)

    2. Relevant equations
    integration by parts

    3. The attempt at a solution

    I am currently in differential equations and I remember from cal II that I have to keep using the equation above until the integral loops around, then set it equal to something,... but I'm foggy on what it's equal to. Any help would be appreciated. thanks.
    Last edited by a moderator: Feb 4, 2012
  2. jcsd
  3. Feb 4, 2012 #2


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    Let's call the integral I. When you do integration by parts repeatedly, you eventually end up with

    I = stuff + (something) I

    At this point, you solve for I.
  4. Feb 4, 2012 #3
    I believe that you should keep integrating by parts until you end up with something that looks like:

    ∫.5e^(t/50)*sin(t) = SOMETHING - ∫.5e^(t/50)*sin(t)

    then you can add ∫.5e^(t/50)*sin(t) to both sides to get:

    2*∫.5e^(t/50)*sin(t) = SOMETHING

    so that

    ∫.5e^(t/50)*sin(t) = (1/2)*SOMETHING

    EDIT: vela beat me to it :smile:
  5. Feb 4, 2012 #4
    thanks. vela helped, and saladsamurai's elaboration was necessary. You guys are lifesavers.
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