Calculus masterpiece

Calculus Level 3

02πexsin(x)cos(x)dx \large \int_0^{2\pi} e^x \sin(x) \cos(x) \, dx

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

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