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Homework Help: Integration by Parts

  1. Oct 23, 2006 #1
    Hi all,

    I am having problems with the integral:

    [tex]\int e^{(ax)} cos(bx) dx [/tex]

    I have got to [tex] \frac{e^{ax} sin(bx)}{b} - \int \frac{a e^{ax} sin(bx)}{b} dx[/tex]

    After this I can only see myself going around in circles.

    Any help would be appreciated. :smile:

    Cheers,

    The Bob (2004 ©)
     
  2. jcsd
  3. Oct 23, 2006 #2
    The integrals should be:

    [tex]\int e^{(ax)} cos(bx) dx [/tex]

    and

    [tex] \frac{e^{ax} sin(bx)}{b} - \int \frac{a e^{ax} sin(bx)}{b} dx[/tex]

    LaTex doesn't seem to be editable anymore. :frown:

    The Bob (2004 ©)
     
  4. Oct 23, 2006 #3

    Office_Shredder

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    Go again, taking the integral on the RHS Since you get a -cos(x), where you would normally have subtraction from your integration by parts you get addition, except the whole thing is negative anyway, so your new integral (which is a bunch of constants times eaxcos(bx) ) turns out negative. Add that to both sides, and multiply/divide by constants to isolate your original integral
     
  5. Oct 26, 2006 #4
    Cheers Office_Shredder. Sorry for the late reply, I have been very busy recently.

    Thanks so much again :biggrin:,

    The Bob (2004 ©)
     
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