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Math Help - int (dx/(1-cosx) ) dx

  1. #1
    Boo
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    int (dx/(1-cosx) ) dx

    Dear All!
    please, coudl you help me with:

    \int \frac{1}{1-cosx}dx=-\frac{cosx+1}{sinx}
    is that ok?
    Many thanks!
    Last edited by Boo; January 26th 2013 at 07:58 AM.
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  2. #2
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    Re: int (dx/(1-cosx) ) dx

    Use the expressions ∫▒cot⁡〖x dx=log⁡|sinx|+C 〗 and ∫▒〖cosec x dx=log⁡〖| cosec x-cotx |+C〗 〗
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  3. #3
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    Re: int (dx/(1-cosx) ) dx

    Multiply numerator and denominator by (1+\cos{x}).

    \int \frac{1+\cos{x}}{(1-\cos{x})(1+\cos{x})}\,dx =

    \int \frac{1+\cos{x}}{1-\cos^2{x}}\,dx =

    \int \frac{1+\cos{x}}{\sin^2{x}}\,dx =

    \int \csc^2{x}\,dx+\int\csc{x}\cot{x}\,dx =

    -\cot{x}-\csc{x}+C

    - Hollywood
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  4. #4
    Boo
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    Re: int (dx/(1-cosx) ) dx

    Many thanks, Hollywood!!!
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