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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