Question

Find the inverse Laplace transform of F (s)=2/s^3

Answer 1

Recall that for integers n > -1,

$L_s\left\{t^n\right\} = \dfrac{n!}{s^{n+1}}$

Then

$\displaystyle L^{-1}_t\left\{\frac2{s^3}\right\} = L^{-1}_t\left\{\frac{2!}{s^{2+1}}\right\} = \boxed{t^2}$