Problem $8in$ Section $8\mathrm{.}1$

Find the Laplace transform $of$ the function

$f(t)=\{\begin{array}{ccc}1& if& 0t<mn>4</mn>\end{array}$

$0ift4$

$L\{f(t)\}=\frac{6}{(s+3{)}^4}+\frac{12}{(s+1{)}^2+9}$

$L\{f(t)\}=\frac{1}{s}(1-\frac{2}{s^2})+\frac{2e^{-s}}{s^2}(1+\frac{1}{s})$

$L\{f(t)\}=\frac{1}{(s+3{)}^2}+\frac{2}{s^2+1}$

$L\{f(t)\}=\frac{1}{s}(1-e^{-4s})$

$L\{f(t)\}=\frac{3}{s}+\frac{1}{s^2}+\frac{2}{(s+1{)}^2+4}$