At my current study level in college, use of inverse Laplace transform is not mentioned well - textbooks say "use tables." So, can anyone show me how to use inverse Lapalce transform? And also proof?
Edit: I am not asking how to use tables to solve inverse Laplace transform - I ACTUALLY want to know how to solve inverse Laplace transform using the inverse Laplace transform formula:
$$f(t) = \mathcal{L}^{-1} \{F(s)\} = \frac{1}{2 \pi i} \lim_{T\to\infty}\int_{ \gamma - i T}^{ \gamma + i T} e^{st} F(s)\,ds$$