# Definite integral of mixtures of irrational numbers

Calculus Level 5

$\large \int_0^1 \dfrac{\tan^{-1}x}{x^{2/3}} \, dx$

Given the integral above equals to

$\pi \left(\dfrac ab - \dfrac{\sqrt c}d \right) + \dfrac ef \ \ln(g)$

where $$a,b,c,d,e$$ and $$f$$ are positive integers with prime $$g$$ and $$\gcd(a,b) = \gcd(c,d) =\gcd(e,f) = 1$$.

Find the value of the 7-digit integer, $$\overline{abcdefg}$$.

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