# Unusual Laplace Transform

Calculus Level 5

Let $$g(s)$$ be the Laplace Transform of the function $$f(x) = \dfrac{1}{\lceil x \rceil}$$.

What is the closed form of $$g$$ using the variable $$s$$?

$\begin{array}{ccc} A: & \dfrac{(1-e^s)\ln(1-e^{-s})}{s} \\ B : & \dfrac{\ln(e^s-1)}{s^2} \\ C : & \dfrac{s \ln(e^s-1)}{e^s-1} \\ D : & \dfrac{\ln(1-e^{-s})}{s(e^{-s}-1)} \end{array}$

Notation: $$\lceil \cdot \rceil$$ denotes the ceiling function.

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