Not So Rational Integration

Calculus Level 5

\[\large I = \int_0^1 \dfrac{(2x-1)\ln x}{1-x^2} \, dx\]

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

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

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