Question

Inverse Laplace transform of \( \cot^{-1}(s) \)

Answer 1

using property no 30)
http://tutorial.math.lamar.edu/Classes/DE/Laplace_Table.aspx

let f(t) = sin(t), n=-1,

\[ \sin(t) / t = -\int L(\sin(t)) ds = -\arctan(s)+c_1 = \cot^{-1}(s) + c_2\]
they only differ by constant.