Calculus masterpiece

Calculus Level 3

\[ \large \int_0^{2\pi} e^x \sin(x) \cos(x) \, dx \]

If the integral above equals to \(\large \frac{A-e^{B\pi}}C \) for integers \(A,B\) and \(C\), then find the value of \(A+B+C\).

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