Inverse Laplace Transform Without Partial Fractions

Today, we evaluate an example of the inverse Laplace transform using only the residue theorem.

Inverse Laplace Transform Formula:

[the_nuwarrior]

I have an idea, in the case of Holomorphic functions that are not polynomials you can aproximate the inverse laplace transform using Padé approximant, it can be usefull to solve non-linear partial diferential equations

[ConnorHearne-we]

Would this work with a denominator such as (x-1)(x+1)^2