Busy Integral

Calculus Level 4

Evaluate

\[\large \displaystyle \int_{0}^{\pi}\dfrac{dx}{5+3\cos^2x}\]

If your answer comes in the form of \(\dfrac{\pi}{a\sqrt{b}}\), where \(a\) and \(b\) are positive integers with \(b\) square-free, find \(a+b\).

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