Find the inverse Laplace transform $f(t)=L^{-1}\left\{F(s)\right\}$ of the function $F(s)=\dfrac{7s−22}{s^2−6s+13}. $

Question

Find the inverse Laplace transform $f(t)=L^{-1}\left\{F(s)\right\}$ of the function $F(s)=\dfrac{7s−22}{s^2−6s+13}. $

$f(t)=L^{-1}\left\{\frac{7s-22}{s^2-6s+13}\right\}$.

I was trying to break $F(s)$ into simpler rational fractions by partial fraction, but I could not factor $s^2-6s+13$. Can anyone give me some hints?

Answer 1

Hint: complete the square.....