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Math Help - indefinite integral

  1. #1
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    indefinite integral

    i have know idea on how to do this problem:

    int csc^{2}(2t)} / sqrt{1 + cot(2t)} dt
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by viet View Post
    i have know idea on how to do this problem:

    int csc^{2}(2t)} / sqrt{1 + cot(2t)} dt
    Is the integrand not very closly related to the derivative of sqrt(1+cot(2t)) ?
    In which case the Fundamental Theorem of Calculus will give the integral.

    Unless I have made some elemenatry mistake:

    d/dt sqrt(1+cot(2t))=(1/2) 2 (-csc^2(2t))/sqrt(1+cot(2t))=-csc^2(2t)/sqrt(1+cot(2t))

    so:

    int csc^{2}(2t)} / sqrt{1 + cot(2t)} dt = -sqrt(1+cot(2t))

    RonL
    Last edited by CaptainBlack; February 15th 2007 at 10:16 PM.
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  3. #3
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    -1/2*4^(1/2)*((sin(2*t)+cos(2*t))/sin(2*t))^(1/2)

    ... i think.
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