$[-/6$ Points$]$

SCALCET$97\mathrm{.}8\mathrm{.}085.$

If $f(t)$ is continuous for $t0,$ the Laplace Transform of $f$ is the function $F$ defined by

$F(s)={\displaystyle \underset{0}{\overset{}{}}}f(t)e^{-st}dt$

and the domain of $F$ is the set consisting of all numbers $s$ for which the integral converges. Find the Laplace transforms of the following functions. $($Enter domains as inequalities.$)$

$($a$)f(t)=31$

$F(s)=$ with domain $$

$($b$)f(t)=5e^t$

$F(s)=$ with domain $$