Integrating Floors And Ceilings

Calculus Level 2

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

\[\] Notations: \( \lfloor \cdot \rfloor \) denotes the floor function and \( \lceil \cdot \rceil \) denotes the ceiling function.