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Math Help - integration: by parts

  1. #1
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    integration: by parts

    \int e^x(\cos{x})dx

    substituted it to

    dv = e^(x) dx
    v = e^(x)

    u = (cos(x))
    u = -sin(x) dx

    and this one goes infinity for me
    help needed for what to sub ... i dunno how the integrator got a short answer
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  2. #2
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    \int e^x(\cos{x})dx

    substituted it to

    dv = e^(x) dx
    v = e^(x)

    u = (cos(x))
    u = -sin(x) dx

    and this one goes infinity for me
    help needed for what to sub ... i dunno how the integrator got a short answer
    Give this integral a name,
    Let X=\int e^x \cos x dx

    After doing integration by parts you get,
    X = \mbox{ something } + \int e^x \sin x dx

    After doing integration by parts again you get,
    X = \mbox{ something } + \mbox{ more something }- \int e^x \cos x dx

    And it seems it goes on forever. But \int e^x \cos x dx = X

    So,
    X = \mbox{ something } + \mbox{ more something } - X

    Thus,
    2X = \mbox{ something } + \mbox{ more something }

    Thus,
    X = \frac{ \mbox{ something }+\mbox{ more something }}{2} + C
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  3. #3
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    thanks alot
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