# This one is not that bad

Calculus Level 4

$\large \int_{\frac{\sqrt 2}2}^1 \dfrac1{x^5 \sqrt{4x^2-1}} \, dx$

If the integral above can be expressed as $$-A + \dfrac {B\sqrt C}A + \dfrac \pi D$$, where $$A$$, $$B$$, $$C$$ and $$D$$ are positive integers with $$A$$ and $$B$$ being coprime integers, and $$C$$ square-free, find $$A+B+C+D$$.

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