# Interesting integral

Calculus Level 3

$\large \int_0^{\infty} \dfrac{1}{\sqrt[\leftroot{-2}\uproot{2}3]{x}(x+1)} \, dx =\dfrac{a\pi}{\sqrt{b}}$

If the equation above holds true for positive integers $$a$$ and $$b$$ such that $$b$$ is square-free, find $$a+b$$.

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