# 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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