Consider Theorem $7\mathrm{.}2\mathrm{.}1as$ given below.

Theorem $7\mathrm{.}2\mathrm{.}1-$ Some Inverse Transforms

$a.1=L^{-1}\{\frac{1}{s}\}$

$b.t^n=L^{-1}\{\frac{n!}{s^{n+1}}\},n=1,2,3,$dots

$c.e^{at}=L^{-1}\{\frac{1}{s-a}\}$

$d.sin(kt)=L^{-1}\{\frac{k}{s^2+k^2}\}$

$e.cos(kt)=L^{-1}\{\frac{s}{s^2+k^2}\}$

$f.sinh(kt)=L^{-1}\{\frac{k}{s^2-k^2}\}$

$g.cosh(kt)=L^{-1}\{\frac{s}{s^2-k^2}\}t.L^{-1}\{\frac{4s}{4s^2+1}\}$