1. ## 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.

2. Originally Posted by C.C.

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

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