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Thread: integral of a+bcosx form

  1. #1
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    integral of a+bcosx form

    This is my first post to this forum, so I wish to start by saying hello to all of you who take time out of your schedule to help those of us with questions. As a teacher, I know how valuable this is! My question involves finding out the technique for solving the following integral:


    $\int {\frac{{\cos xdx}}{{{{\left( {a - b\cos x} \right)}^2}}}}$


    According to a German table of integrals, I have found the following clue:


    $\int {\frac{{\cos xdx}}{{{{\left( {a + b\cos x} \right)}^2}}}} = \frac{1}{{{a^2} - {b^2}}}\left( {\frac{{a\sin x}}{{a + b\cos x}} - b\int {\frac{{dx}}{{a + b\cos x}}} } \right)$


    I have tried a number of different approaches, but I have not found a step by step solution to the integral. Any suggestions would be appreciated!
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  2. #2
    MHF Contributor

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    Re: integral of a+bcosx form

    Do you have any reason to believe that can be integrated in closed form?
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  3. #3
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    Re: integral of a+bcosx form

    I probably should have worked on the problem for a couple more days before posting, because I was able to solve the integral at last. I ended up using a partial fraction decomposition to split it into two integrals, then used a recurrence formula technique to solve the first of the two integrals, and finally a Weierstrass substitution to solve the second integral.
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