Can someone help evaluate the following integral? (I have tried doing it with Mathematica but I just get the integral back - I am assuming that it can't figure out how to solve it?)
\begin{equation} I=\int \frac{\csc ^2(\pi f) (\sin (2 \pi f))^{2a}}{-2 \cos (2 \pi a f)+\cos (2 \pi f-2 \pi a f)-2 \cos (2 \pi f)+3} \, df \end{equation}
$a(>>1)$ is just a constant.
Some context:
The above integral is actually the result of a particular electrical circuit which implements the following $Z$ domain transfer function:
$\begin{equation} H(z)= \frac{\left(1-z^{-a}\right)^2}{\left(1-z^{-1}\right) \left(2-z^{-a}-z^{-1}\right)} \end{equation}$
where $z=e^{2\pi i f}$. In order to find the total power at the output, I need to evaluate the following integral:
$\begin{equation} \int_{f=0}^{f=f_s} |H(z)|^2 df \end{equation}$
The integral that you see in the first equation is actually the above function ($|H(z)|^2$) after simplification by Mathematica.
