Perform a Laplace transform on the following functions:

a$.f(t)=e^{4t}-t^7-t^3-sin(6t)$

b$.f(t)=15e^{4t}cos(3t)-3e^{6t}sin(2t)$

c$.f(t)=\{\begin{array}{cc}0,& t<mn\; id="EditorElement\_411242">0</mn>\\ 12,& 0t<mn\; id="EditorElement\_411263">9</mn>\\ 0,& t>9\end{array}$

Perform an inverse Laplace transform on the following functions:

a$.F(s)=\frac{8}{s^2+64}$

b$.F(s)=\frac{s+2}{(s+1{)}^2}$

C$.F(s)=\frac{1}{s^8}$