# Typical Indefinite Integration!

Calculus Level 5

$\large \int \frac{\cos(2016x)}{\sin(x)} \, dx$

Let $$x$$ be a real number except at multiples of $$\pi$$. Ignoring the arbitrary constant, if the indefinite integral is equals to

$\large I = \alpha \left( \sum_{n=1}^{1008} \frac{ \cos((2n-1)x)}{2n-1} \right) + \ln \left| \tan \left( \frac {2x}\beta \right) \right |$

For constants $$\alpha$$ and $$\beta$$, evaluate $$\alpha^\beta - \beta^\alpha$$.

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