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 \(\alpha^\beta - \beta^\alpha \).
by
Satyajit Mohanty