Exercise $1\mathrm{.}1\mathrm{.}1.$ Obtain the Laplace transforms of the following functions from first principles, by carrying out the appropriate integration, and find the value of ${}_e$ :

a$)y=2$

b$)x=4e^{-8t}$

c$)x=-0\mathrm{.}6e^{3t}$

d$)y=2+e^t$

e$)f(t)=2e^{-3t}-3e^{2t}$

f$)y=2t$

g$)f(t)=t{e}^t$

h$)x=5-3t$