Let $f(t)be$ a function $on[0,).$ The Laplace transform $offis$ the function $F$ defined $by$ the integral $F(s)={\displaystyle \underset{0}{\overset{\phantom{}}{}}}{e}^{-st}f(t)dt.$ Use this definition $to$ determine the Laplace transform $of$ the following function.

$F(s)F(s)={\displaystyle \underset{0}{\overset{3}{}}}{e}^{(5-s)t}dt+{\displaystyle \underset{3}{\overset{}{}}}4e^{-st}dtf(t)F(s)=\begin{array}{cc}{e}^{15-3s}-1& 4e^{-3s}\\ ?& \text{f}\text{o}\text{r}\text{a}\text{l}\text{l}\text{p}\text{o}\text{s}\text{i}\text{t}\text{i}\text{v}\text{e}s\end{array}5$ where $F(5)=4..1.$ PLEASE show all work and I will upvote $if$ correct. Thank you@