# What would the laplace inverse of a laplace be?

1. Nov 15, 2015

### Jim wah

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

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

2. Nov 22, 2015

### Staff: Mentor

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

Last edited: Nov 23, 2015
3. Nov 22, 2015

### HallsofIvy

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

Last edited by a moderator: Nov 23, 2015