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Math Help - Integrating By Parts

  1. #1
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    Integrating By Parts

    My brain has apparently turned to mush since last summer.

    \int{(3t+5)cos(t/4)}dt

    I took...

    <br />
u=3t+5<br />
    and...
    <br />
dv=cos(t/4)<br />

    I need help going from there to...

    <br />
du=<br />
    and
    <br />
v=<br />

    the tutorial I'm using skips the intervening steps and just gives me v and du. I want to understand the underlying process. Acctual steps to get to du and v would be greatly appreciated. Thanks anyone and everyone
    Last edited by brazedowl; June 27th 2010 at 06:30 AM. Reason: Getting used to Latex
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  2. #2
    MHF Contributor chisigma's Avatar
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    near Piacenza (Italy)
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    Perhaps the best way is to compute separately...

    \displaystyle \int (3t + 5)\ \cos \frac{t}{4}\ dt = \int 5 \ \cos \frac{t}{4}\ dt + \int 3 t\ \cos \frac{t}{4}\ dt (1)

    The first integral doesn't require integration by part and its result is useful for the second integral...

    Kind regards

    \chi \sigma
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  3. #3
    Junior Member slider142's Avatar
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    To get du, differentiate the expression for u. Similarly, to get v, integrate the expression for dv.
    Note that as chisigma says, there is no reason to choose 3t + 5 as u, since the integral can be simplified first.
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