Find the function from numbers

Calculus Level 3

Let \(f:(1,+\infty)\to \mathbb R\) be a continuous function such that:

\[\int_{2}^{150} (x-1)\ln(x-1)(2f(x)-(x-1)\ln(x-1))dx=\int_{2}^{150}f^{2}(x)dx\]

If \(f(101)=A\), enter \(\lfloor A\rfloor\) as your answer.

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

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