Help finding inverse laplace transform?

[Chandasouk]

http://img215.imageshack.us/i/unledc.jpg/

Using the residue method, I found K1 and K2 to be -2 and 4 respectively. However, where do I go from there?

 

[n.karthick]

It is already mentioned in the figure you have attached.
Substitute two values for s say s=0 and s=1 independently and get two equations in terms of k3 and k4. So now 2 equations and 2 unknowns. You can solve and get values of k3 and k4.
Once you found the values of all constants, you can find inverse LT for each fractional term.