The Laplace Transform of the current in a certain series circuit is:
Invert the Laplace Transform to find the expresion for the current I(t), not
by partial fraction expansion, but by completing the square in the denominator,
dividing the expression for 
in two and using two entries from your
table of Laplace Transforms.
What was the circuit and the input voltage in this case ?
SOLUTION :
Using:
with a=1 and 
:
To find a circuit this might represent, multiply out the fraction in the Laplace Transform:
The reason for dividing by s was to give the LHS the form of the Laplace Transform of a series LRC circuit:
So the series LRC circuit would have the component values L=1henry
, R=2ohm and C=0.2farad.
Then the RHS is the Laplace Transform of the input voltage.
So the input voltage is a 7volt step function plus a unit delta function (at t=0).