# A Big Nope!

Calculus Level 5

$\large \int \frac {dx}{ 2x\sqrt{1-x} \sqrt{2 - x + \sqrt{1-x} } }$

If the indefinite integral above can be expressed as

$A \ln (z + B + \sqrt{z^2+3z+3} ) + C \ln(s + A + \sqrt{s^2-s+1})$

where $$z = \dfrac1{\sqrt{1-x} - 1}$$ and $$s= \dfrac1{\sqrt{1-x} + 1}$$ and $$A,B$$ and $$C$$ are constants, find the value of $$2(A+B+C)$$.

Assume we ignore the arbitrary constant of integration.

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