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Math Help - Integrals - first by substitution then by parts

  1. #1
    dsspence
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    Integrals - first by substitution then by parts

    we're given the integral 2cos(ln(x))dx

    and told to first use substitution then integration by parts, could someone kindly point me in the right direction
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  2. #2
    MHF Contributor
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    Quote Originally Posted by dsspence
    we're given the integral 2cos(ln(x))dx

    and told to first use substitution then integration by parts, could someone kindly point me in the right direction
    Right direction?
    Okay, go to the Calculus thread in this forum, look for the posting by nirva, "Some calc questions". Open that. The second problem there is almost the same as yours, except that yours has "2" before the cos(ln(x)).
    If you know what to do with that "2", and you could follow the solution there of that second problem, then you should be able to get your integral.
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  3. #3
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    Quote Originally Posted by dsspence
    we're given the integral 2cos(ln(x))dx

    and told to first use substitution then integration by parts, could someone kindly point me in the right direction
    You have,
    \int \cos (\ln x) dx=\int \frac{x\cos (\ln x)}{x}<br />
    Use substitution u=\ln x then, u'=1/x and x=e^u
    Thus,
    \int e^u \cos u \frac{du}{dx} dx=\int e^u \cos u du

    ----
    I am going to stop here because I realized that ticbol made a post before me and already answered this question. Do as he says.
    Last edited by ThePerfectHacker; May 17th 2006 at 06:55 PM.
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