Laplace Transform

$F(s)={\mathcal {L}}\left\{1\right\}=\int _{0}^{\infty }e^{-st}\,dt=$ ${\frac {1}{s}}$

$F(s)={\mathcal {L}}\left\{t^{2}\right\}=\int _{0}^{\infty }e^{-st}t^{2}\,dt=$ ${\frac {n!}{s^{n+1}}}$