Not So Rational Integration

Calculus Level 5

I=01(2x1)lnx1x2dx\large I = \int_0^1 \dfrac{(2x-1)\ln x}{1-x^2} \, dx

Find the value of the closed form of the above integral II.
Submit your answer as 24I\lfloor 24I \rfloor.

Notation: \lfloor \cdot \rfloor denotes the floor function.

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