I tried this:

InverseLaplaceTransform[-((-6.5 - 3.25 s - 5.5 s^2 + 0.5 s^3 + 
      s^4)/((2 + s) (1 + 0.5 s + s^2) (1.5 + s + s^2))), s, t] // 
   Simplify // ComplexExpand // Simplify

In this way I get the following:

0.714286 E^(-2. t) - 1.71429 E^(-0.5 t) Cos[(1.11803 + 0. I) t] + 
 3.19438 E^(-0.5 t) Sin[(1.11803 + 0. I) t]

which is similar to the answer I want:

$ [0.7143 e^{-2t}-1.7145 e^{-0.5t}cos(1.25t)+3.194 e^{-0.5t}sin(1.25t)]u(t) $

I have tried with FullSimplify, Apart, TrigReduce, ExpToTrig and I have not got the answer in terms of the UnitStep function.

I will appreciate any suggestion to get the answer I want.