\[\large \displaystyle \left \lfloor 10^5 \int_{0}^{\infty}{\frac{-\ln(1+e^{-\pi x})}{1+x^2} \ dx} \right \rfloor = \ ?\]

**Details and Assumptions:**

- \(\left \lfloor x \right \rfloor\) denotes the floor or greatest integer function.

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