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∫cos(2016x)sin(x) dx \large \int \frac{\cos(2016x)}{\sin(x)} \, dx ∫sin(x)cos(2016x)dx
Let xxx be a real number except at multiples of π\piπ. Ignoring the arbitrary constant, if the indefinite integral is equals to
I=α(∑n=11008cos((2n−1)x)2n−1)+ln∣tan(2xβ)∣ \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 | I=α⎝⎛n=1∑10082n−1cos((2n−1)x)⎠⎞+ln∣∣∣∣∣tan(β2x)∣∣∣∣∣
For constants α\alpha α and β\beta β, evaluate αβ−βα\alpha^\beta - \beta^\alpha αβ−βα.
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