# 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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