Interesting Integrals 8

Calculus Level 4

\[\large \int_{0}^{\pi/4}\dfrac{\sin(x) + \cos(x)}{3 + \sin(2x)}\,dx\ = \dfrac{\ln r}{w}\]

The equation above holds true for coprime positive integers \(r\) and \(w\), find \(r-w\).

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