Partial Sine

Calculus Level 3

π/43π/4x1+sin(x)dx \large \int_{\pi/4}^{3\pi/4} \dfrac x{1+\sin(x)} \, dx

If the integral above equals to π(AB) \pi(\sqrt A - \sqrt B) for positive integers AA and BB, find the value of A+BA+B.

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