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\} = (n!)/(s^(n+1))`

Then

`\displaystyle L^(-1)_t\left\{\frac2{s^3}\right\} = L^(-1)_t\left\{(2!)/(s^(2+1))\right\} = \boxed{t^2}`