Let $f$ be a function defined for $t0.$ Then the integral

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

is said to be the Laplace transform of $f,$ provided that the integral converges.

$f(t)=\{\begin{array}{cc}8,& 0t<mn>3</mn>\\ 0,& t3\end{array}$

Complete the integral$($s$)$ that defines $L\{f(t)\}.$

$L\{f(t)\}={\displaystyle \underset{0}{\overset{\phantom{}}{}}}()dt{\displaystyle \underset{\phantom{}}{\overset{}{}}}()dt$

Find $L\{f(t)\}.($Write your answer as a function of s$.)$

$)>(0$