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Math Help - Integration Help

  1. #1
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    Integration Help

    Hi

    I am working on how to get the last closed field lines of a moving magnetic field (as a bit of background). Anyhow, as part of it, I have to integrate
     \frac{c\Omega \cos(K)+\sin(K)(c^2+\Omega^3K)}{2c^2\Omega(\cos(K) +K \sin(K)}dK

    Anybody have any ideas how I would go about doing this?
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  2. #2
    Super Member General's Avatar
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    Re: Integration Help

    c and \Omega are assumed to be constants? or they are defined in terms of K?
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  3. #3
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    Re: Integration Help

    c and Omega are constants. Everything except K is a constant.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Integration Help

    The denominator is not clear, is it:
    2c^2\Omega[\cos(K)+K\cdot \sin(K)]
    Or
    2c^2\Omega[\cos(K)]+K\cdot \sin(K)
    ?
    Maybe it's useful to split the fraction in two fractions with the same denominator.
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Integration Help

    Quote Originally Posted by Siron View Post
    The denominator is not clear, is it:
    2c^2\Omega[\cos(K)+K\cdot \sin(K)]
    Or
    2c^2\Omega[\cos(K)]+K\cdot \sin(K)
    ?
    Maybe it's useful to split the fraction in two fractions with the same denominator.
    The frightening capital letter, omega make the problem to look scary...

    Prove that:

    \int x\sin{x}\;dx=\sin{x}-x\cos{x}+C
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Integration Help

    Quote Originally Posted by Also sprach Zarathustra View Post
    The frightening capital letter, omega make the problem to look scary...

    Prove that:

    \int x\sin{x}\;dx=\sin{x}-x\cos{x}+C
    That can be proved with integration by parts.
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  7. #7
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    Re: Integration Help

    Sorry, I left out a bracket in my original post . I have also changed it so that you no longer have to deal with Omega .

     \frac{cA \cos(K)+\sin(K)(c^2+A^3K)}{2c^2A(\cos(K) +K \sin(K))}dK

    Ok, so \int x\sin{x}\;dx=\sin{x}-x\cos{x}+C

    Let x=u, dv=sin(x) then you have that v=-cos(x) and  \int x\sin{x}\;dx=-x \cos(x) -\int \cos(x) dx=\sin(x)-x\cos(x) +C

    Sop how does that help with my original equation?
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