Answer
$e^{3t} \cos (2t)+\dfrac{3}{2} e^{3t} \sin (2t) $
Work Step by Step
Since, $F(s)=\dfrac{s}{(s-3)^2+4}$
The inverse Laplace transform of function can be expressed as:
$F(t)=L^{-1} [ \dfrac{s-3}{(s-3)^2+4} ]+L^{-1} [ \dfrac{3}{(s-3)^2+4} ] $
Now, apply the first shifting Theorem.
$f(t)= e^{3t} \cos (2t)+\dfrac{3}{2} e^{3t} \sin (2t) $
