# Integral Cake Delivery III

Calculus Level 3

$\large \int_0^{\pi /4} \dfrac{ x + \sin x}{1 + \cos x} \, dx$

If the value of the integral above is equal to $$\dfrac \pi a (\sqrt b - c)$$, where $$a,b$$ and $$c$$ are positive integers, find $$a+b+c$$.

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