$9\mathrm{.}21.$ Determine the Laplace transform and the associated region of convergence and pole zero plot for each of the following functions of time:

$($a$)x(t)=e^{-2t}u(t)+e^{-3t}u(t)$

$($b$)x(t)=e^{-4t}u(t)+e^{-5t}(sin5t)u(t)$

$($c$)x(t)=e^{2t}u(-t)+e^{3t}u(-t)$

$($d$)x(t)=t{e}^{-2|t|}$