\[\int \left [ \csc^{-1} \lfloor 1+ \sin^2(x) \rfloor + \tan^{-1} \left( \frac{\phi \cos(x)}{1 - \phi \sin(x)} \right) - \cot^{-1} \left( \frac{\cos(x)}{\phi - \sin(x)} \right) \right ] \, dx \]

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