# Reflect on Euler

Calculus Level 5

If

$\int\limits_0^1 \frac{(\ln x)^2}{x-1}\left[ x^{-1/3} - x^{-2/3} \right]\,\mathrm dx$

can be expressed in the form $$\dfrac{A\pi^n}{B\sqrt{C}}$$, where $$A,B,C$$ and $$n$$ are positive integers with $$A$$ and $$B$$ coprime as well as $$C$$ squarefree, then find $$A+B+C+n$$.

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