How Do You Inverse Laplace Transform an RLC Circuit Equation?

[struggling1]

Homework Statement

Derive an equation to represent the current flowing in an RLC circuit where R=12 L=1.2 C=30microfrards with an impulse voltage input. Assume zero conditions when the switch is closed.

Homework Equations

The Attempt at a Solution

I have used the voltage to equal 1, laplace transformed the RLC values and started from basic Kirschoffs law to give
I= s/(1.2s^2+12s)+1

To complete this I know I need to inverse laplace it but cannot get this equation into a format to do it. Can anyone please help before I pull my hair out how to do this??

 

[danago]

1/(1.2s + 12) = (1/1.2) / (s+12/1.2) is of the form a / (s+b) which can be found on any standard table of inverse laplace transforms.

The inverse laplace transform of 1 is the dirac delta function.