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Math Help - Integral cot2x

  1. #1
    Xei
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    Integral cot2x

    Hiyah, how do I work out the integral of cot^2(x)dx?

    I worked out that the differential cotxdx is -csc^2(x) and apparently this is supposed to help.

    I've tried all sorts of perverted methods but they're going nowhere. Any clues?

    Cheers.
    Last edited by Xei; April 18th 2008 at 11:16 AM.
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  2. #2
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    Hello, Xei!

    \int \cot^2\!x\,dx
    Recall that: . \csc^2\!\theta \;=\;\cot^2\!\theta+1 \quad\Rightarrow\quad \cot^2\!\theta \;=\;\csc^2\!\theta - 1

    Then we have: . \int \cot^2\!x\,dx \;=\;\int(\csc^2\!x - 1)\,dx \;=\;\int\csc^2\!x\,dx - \int\,dx

    Got it?

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  3. #3
    Xei
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    Ohhh that was quite obvious.

    Right so

    -\int-\csc^2{x}+1dx=-\cot{x}-x

    ?
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  4. #4
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    Quote Originally Posted by Xei View Post
    Ohhh that was quite obvious.

    Right so

    -\int-\csc^2{x}+1dx=-\cot{x}-x

    ?
    + C.

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  5. #5
    Xei
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    Grah screw +C.

    Cheers.
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