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Math Help - Half-Angle Identities

  1. #1
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    Half-Angle Identities



    I was wondering if I could get some help on how to start to evaluate this integral.

    I started out with changing the secant to (1+tan^2x)^5*sec^2x, but I'm not sure how to deal with the cotangent and the overall structure of this equation.

    Help very much appreciated.
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by C.C. View Post


    I was wondering if I could get some help on how to start to evaluate this integral.

    I started out with changing the secant to (1+tan^2x)^5*sec^2x, but I'm not sure how to deal with the cotangent and the overall structure of this equation.

    Help very much appreciated.

    \int_{0}^{\frac{\pi}{4s}} \frac{\sec ^{12} (16x)}{\cot (16x) } dx


    \int_{0}^{\frac{\pi}{4s}} \frac{1}{\cos ^{12} (16x) \frac{\cos (16x)}{\sin (16x)} } dx

    \int_{0}^{\frac{\pi}{4s}} \frac{ \sin (16x)}{\cos ^{13} (16x) } dx

    let u=\cos (16x) \Rightarrow du = -16\sin (16x) dx \Rightarrow dx = \frac{du}{-16\sin (16x) }

     \int \frac{-1}{16u^{13}} du

    you can continue right
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  3. #3
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    Your explanation is very clear. I can continue. Thank you so much!
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