Question

laplace inverse ln((S+6)/(S+2)

Answer 1

It might help to know this:
\[\mathcal{L}^{-1}\left\{\frac{d^n}{ds^n}F(s)\right\}=(-t)^nf(t)\]
In particular,
\[\mathcal{L}^{-1}\left\{\ln\frac{s+6}{s+2}\right\}=(-t)^{-1}\mathcal{L}^{-1}\left\{\frac{d}{ds}\ln\frac{s+6}{s+2}\right\}=-\frac{1}{t}\mathcal{L}^{-1}\left\{\frac{1}{s+6}-\frac{1}{s+2}\right\}\]
Piece of cake from here.