Inverse Laplace Transform with e^{a s}

[Ricardo Jesus]

Homework Statement

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.

Homework Equations

$L{f} = F(s)$
$L{f*g} = F(s)G(s)

 

[MisterX]

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?