Question: Inverse Laplace Transform sort of works and sort of doesn't. Why?

Here are 4 statements that attempt to use invlaplace on the exponential function. Two work, two don't.

Does anyone know why the two that don't work do that?

Thank you.

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with(inttrans);
[addtable, fourier, fouriercos, fouriersin, hankel, hilbert,   invfourier, invhilbert, invlaplace, invmellin, laplace, mellin,   savetable]
invlaplace(exp(-s),s,t);
                          Dirac(t - 1)
invlaplace(exp(s),s,t);
                    invlaplace(exp(s), s, t)
invlaplace(exp(s),s,t) assuming s<0,s::real;
                    invlaplace(exp(s), s, t)

invlaplace(exp(-s),s,t) assuming s<0,s::real;
                          Dirac(t - 1)
What is going on here?
 

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