Integrating Floors And Ceilings

Calculus Level 2

1812ln1xdx=?\large \int_{\frac{1}{8}}^{\frac{1}{2}} \left \lfloor \ln \left \lceil \dfrac{1}{x} \right \rceil \right \rfloor dx = \, ?

Notations: \lfloor \cdot \rfloor denotes the floor function and \lceil \cdot \rceil denotes the ceiling function.

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