I am trying to find the inverse Laplace transform of expressions of the form $$\frac{a + b \sqrt{s}}{cs + d\sqrt{s} +e}$$ Even an instance of it like $$\frac{\sqrt{s}}{s + \sqrt{s} +1}$$ perhaps? There are similar questions previously asked. Is contour integration the only viable approach or is there a solution for a such or more general family already existent in the literature?
2026-04-12 15:12:50.1776006770
Inverse Laplace with square root of s in quotient
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