Consider the function $\displaystyle F(s) = \frac{8s^{2}+s+5}{s^{3}+s}$.

1. Find the partial fraction decomposition of $F(s)$:
   
   $\displaystyle \frac{8s^{2}+s+5}{s^{3}+s} =$ +
   
   
2. Find the inverse Laplace transform of $\displaystyle F(s)$.
   
   $\displaystyle f(t) = {\mathcal L}^{-1} \left\lbrace F(s) \right\rbrace =$ help (formulas)