we are given with
[tex] f(s)=\frac{2s+8}{s^2+13}\\
\\ [/tex]
Re-write in the expanded form as below
[tex] f(s)=2*\frac{s}{s^2+13}+8*\frac{1}{s^2+13}\\
\\
\text{Now take inverse Laplace Transform on both the sides we get}\\
\\
L^{-1}[f(s)]=L^{-1}[2*\frac{s}{s^2+13}+8*\frac{1}{s^2+13}]\\
\\
L^{-1}[f(s)]=2*L^{-1}\frac{s}{s^2+13}+8*L^{-1}\frac{1}{s^2+13}\\
\\
\text{From the Laplace inverse transform table we can re-write above equation as }\\
\\
f(t)=2cos\sqrt{13}t+ \frac{Sin\sqrt{13}t}{\sqrt{13}} \\ [/tex]
