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What would the laplace inverse of a laplace be?

  1. Nov 15, 2015 #1
    For example:
    If F(s) = L{t3e-16tcos(3t)sin2(t)}

    What would L-1{F(s)} be?
  2. jcsd
  3. Nov 22, 2015 #2


    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
  4. Nov 22, 2015 #3


    User Avatar
    Science Advisor

    [itex]F(s)= L[t3e^{-16t}cos(3t)sin^2(t)][/itex] seem perfectly reasonable to me. A standard definition of the Laplace transform is
    [tex]F= \int_0^\infty e^{-st}f(t)dt[/tex]
    so that the Laplace transform of a function of t is a function of s.
    Last edited by a moderator: Nov 23, 2015
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