Problem $2$: Find x$($t$)$ if X$($s$)$ is given as below.

a$)$ X$($s$)=$es

s$+1$ with ROC: Re$\{$s$\}>1$

Hint: Invert $1$

s$+1$ first and use properties of Laplace transform.

b$)$ X$($s$)=1$

s$2$

$1$ with ROC:$1<$ Re$\{$s$\}<1$

c$)$ X$($s$)=3$s$+5$

$($s$1)2$ with ROC: Re$\{$s$\}>1$