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Thread: integration by parts

  1. #1
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    integration by parts

    integration by parts-capture.png


    I cannot seem to figure this out... I separated the two integrals andd integration by parts , but i end up stuck with figuring out how to do the integration by parts for the first integral.. can someone help me out?
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  2. #2
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    Re: integration by parts

    For the first integral, you will take $u=f(x)$.
    For the second, you will take $\mathrm dv = f''(x) \mathrm dx$.

    In each case, you will get $\int f'(x)\cos{(3x)} \, \mathrm dx$ as your integral on the right hand side. Making this integral the subject of each equation, you will find two expressions that must be equal and can be manipulated to get your result.
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