Inte-greater!

Calculus Level 4

π/6π/6sinxsinxcosxdx=πA+12ln(BC)\large \int _{ - \pi / 6 }^{ \pi / 6 }{ \cfrac { \sin x }{ \sin x - \cos x } } \, dx = \, \dfrac{\pi}{A} + \dfrac{1}{2} \, \ln (B-\sqrt C )

Given AA, BB and CC are positive integers satisfying the equation above, find A+B+CA+B+C.

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