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Math Help - Negative Exponent Trigonometric Integrals

  1. #1
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    Negative Exponent Trigonometric Integrals

    I've run into a couple of integrals I didn't know how to solve. I managed to find the solution to only one of them (INTEGRAL 1/sin x = - ln |csc x + cot x| + C)

    I'd like help with the following, (kind of urgent - doing some tutoring and need to clear up stuff like this in case it comes up):

    1. INTEGRAL 1/sin
    ^2 (x)
    2. INTEGRAL 1/cos^2 (x)

    I'm guessing the solutions for both are similar..and I'm assuming there may be a formula for integrals such as sin^- n (x) (or cos), but I'm mostly interested in the exponent - 2.

    Thanks in advance to anyone who gives it a shot!
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  2. #2
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    \frac{1}{{\sin ^2 (x)}} = \csc ^2 (x)\,\& \,\frac{1}{{\cos ^2 (x)}} = \sec ^2 (x)<br />
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  3. #3
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    Yeah, I can figure as much... but it's the SOLVING part that I'm not sure of. Obviously, 1/sin x = csc x, so if I know the integral of one, I know the other... I guess I could have reformulated my question to read INTEGRAL csc^2 (x) and INTEGRAL sec^2 (x)..but the solving of those integrals is what I need help with. Links to solutions or solutions themselves are fine.

    Thanks for helping!
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Doky53 View Post
    Yeah, I can figure as much... but it's the SOLVING part that I'm not sure of. Obviously, 1/sin x = csc x, so if I know the integral of one, I know the other... I guess I could have reformulated my question to read INTEGRAL csc^2 (x) and INTEGRAL sec^2 (x)..but the solving of those integrals is what I need help with. Links to solutions or solutions themselves are fine.

    Thanks for helping!
    Look here on the third page...it will help you with all sorts of trigonometric integrals

    http://www.mathhelpforum.com/math-he...-tutorial.html
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