or, in other words:
now just look up the rules in the table of your text. what are the inverse Laplace transforms for the guys in red?
with some algebraic manipulation (completing the square of the denominator, factoring out a minus 1 from the numerator and writing -1 as 4 - 5) we find that this expression is:and
now this is the same story as the last one. look up the transforms in the table in your text