# You can't guess what's coming next!

Calculus Level 5

$\displaystyle \large\int_{0}^{\infty}{\frac{dx}{{x}^{2/3}(1+\sqrt{2}x+{x}^{2})}}$

If the integral above evaluates to $$\displaystyle \frac{{\pi}^{a}\sqrt{b}}{c}$$ for positive integers $$a,b,c$$ with $$b$$ square-free, then submit your answer as $$a+b+c$$.

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