$$L ^ { - 1 } [ \log ( \frac { s ^ { 2 } + 1 } { s ( s + 1 ) } ) ]$$
$\frac{\log(\frac{s^{2}+1}{s\left(s+1\right)})}{L}$
$-\frac{\log(\frac{s^{2}+1}{s\left(s+1\right)})}{L^{2}}$