$(24$ points$)$ Find the inverse Laplace $of$ the following:

$(a)F(s)=\frac{3s^2{e}^{-s}+2}{s^2}$

$(b)G(s)=\frac{3s-5}{s-1}+\frac{e^{-2s}}{s-3}$

$(c)H(s)=\frac{6s-5}{s^2+7}$

$(d)F(s)=\frac{6}{s}-\frac{1}{s-8}+\frac{4}{s+3}$

$(e)G(s)=\frac{3s-2}{2s^2-6s-2}$

$(f)H(s)=\frac{s^2}{s^2+1}$

$(5$ points$)$ Find the general solution $to$

$2y^{\text{'}\text{'}}+18y=6tan(3t).$

Hint: $If$ stuck, try multiplying with $\frac{sec(x)+tan(x)}{sec(x)+tan(x)}.$