# Party time integral!

Calculus Level 5

$\large \int_0^{\frac\pi4} \sqrt[3]{\tan(x)} \, dx$

If the value of the integral above is equals to $$\dfrac{\sqrt a }b \pi - \dfrac1c \ln(2)$$ for positive integers $$a,b$$ and $$c$$ with $$a$$ square-free, find the value of $$a+b+c$$.

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