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Homework Help: Inverse Laplace Transform with e^{a s}

  1. Apr 8, 2015 #1
    1. The problem statement, all variables and given/known data
    How can I take the Inverse Laplace Transform of $F(s) = \frac{d}{ds}\left(\frac{1-e^{5s}}{s}\right)$?
    I have tried going with inverse of the derivative and convolution (even tried evaluating the derivative and go from there) but although I can get to some results none of them seems to make sense to me, as for example $f(t) = t(H_{-5} - 1)$, though I don't think this is even correct. Any help is greatly appreciated.

    2. Relevant equations
    $L{f} = F(s)$
    $L{f*g} = F(s)G(s)
  2. jcsd
  3. Apr 8, 2015 #2
    Should that be
    $$F(s) = \frac{d}{ds}\left(\frac{1-e^{-5s}}{s}\right)$$
    In that case ##t(H(t-5) - 1) ## should be correct (for t>0). As written above (without the minus in the exponent) the inverse expression does not converge. What is causing you uncertainty?
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