Using the definition, find the following Laplace transforms.

$($a$)$ Find the bilateral Laplace transform of $x(t)=$exp$(2t)u(3-t).(10$ points$)$

$($b$)$ Find the unilateral Laplace transform of $x(t)=sin(2t+3)u(t).($hint: Using Euler's formula, rewrite $sin(2t+3)$ as the summation of complex exponentials first$).$ You can leave your unilateral transform in exponential form, but clearly indicate the ROC. $(12$ points$)$Using the definition, find the following Laplace transforms.

$($a$)$ Find the bilateral Laplace transform of $x(t)=$exp$(2t)u(3-t).(10$ points$)$

$($b$)$ Find the unilateral Laplace transform of $x(t)=sin(2t+3)u(t).($hint: Using Euler's formula, rewrite $sin(2t+3)$ as the summation of complex exponentials first$).$ You can leave your unilateral transform in exponential form, but clearly indicate the ROC. $(12$ points$)$