I'm after the numerical inverse Laplace transform of a function, so I type
f[t_?NumericQ] := InverseLaplaceTransform[1/(1 + s + ArcTanh[1/(s - 1)]), s, t];
This function may possibly suck, but it looks like its inverse Laplace transform should exist, albeit not in closed form (for instance, by the initial value theorem we know that
f[t->0+]=1). However, when confronted with this task Mathematica simply replicates my command without giving a numerical solution.
ArcTanh is a multivalued function in the complex plane, but shouldn't the algorithm used for Laplace inversion know how to handle this?