# Why all integration problems have integrand?

Calculus Level 5

$\displaystyle\int_{-\pi/3}^{\pi/3} \dfrac{\pi+4x^3}{2-\cos\left(|x|+\frac{\pi}{3}\right)}\ dx$

If the above integral can be expressed as $$\dfrac{a\pi}{\sqrt{b}} \tan^{-1} \left(\frac{1}{c}\right)$$ for positive integers $$a,b,c$$ with $$a,b$$ coprime and prime $$c$$. Find $$a+b+c$$.

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