What would the laplace inverse of a laplace be?

[Jim wah]

For example:
If F(s) = L{t³e^-16tcos(3t)sin²(t)}

What would L^-1{F(s)} be?

 

[Mark44]

For example:
If F(s) = L{t³e^-16tcos(3t)sin²(t)}

What would L^-1{F(s)} be?

If $\mathcal{L}[f(t)] = F(s)$, then $\mathcal{L}^{-1}[F(s)] = \mathcal{L}^{-1}[\mathcal{L}[f(t)]] = f(t)$

 

[HallsofIvy]

$F(s)= L[t3e^{-16t}cos(3t)sin^2(t)]$ seem perfectly reasonable to me. A standard definition of the Laplace transform is
$$F<s>= \int_0^\infty e^{-st}f(t)dt</s>$$
so that the Laplace transform of a function of t is a function of s.