Find the inverse laplace (if there is one)

Question

I need to find if $F(s)$ can be a laplace transform of a continuous exponential function:

$$F(s)=\frac{s^3}{s^3+2s^2+s+1}$$

any ideas?

Answer 1

As Ian suggests, because of the equal polynomial orders in the numerator and the denominator, the inverse implicates the Dirac delta function. So the answer is no, F(s) is not a transform of a continuous exponential function.