Find the inverse Laplace transform of

$\displaystyle {F}{\left({s}\right)}=\frac{{1}}{{s}}-\frac{{s}}{{{s}^{{2}}+{1}}}+{e}^{{-\frac{\pi}{{2}}{s}}}{\left(\frac{{{3}{s}-{1}}}{{{s}^{{2}}+{1}}}\right)}$

Note: Use $\displaystyle {u}$ for the step function.