Answer
See below
Work Step by Step
Since, $y(s)=\dfrac{1}{s+2} +\dfrac{1}{s-2}+\dfrac{3}{(s-2)^2}$
The inverse Laplace transform of function can be expressed as:
$y(t)=L^{-1} [\dfrac{1}{s+2} +\dfrac{1}{s-2}+\dfrac{3}{(s-2)^2}]$
Now, apply the first shifting Theorem.
$f(t)= e^{-2t} +e^{2t} +3te^{2t} $
