Thread: Stuck on Inverse Transform

I am getting stuck trying to find the inverse laplace transform...I've checked it against the tables, and nothings looking familiar...Am I missing a trick here?!

Thank you in advance!

How about express it in terms of partial fractions first then take the inverse transform of those terms? I would think we could treat the complex roots just like regular constants and work it through and get an expression containing those complex numbers. If it were part of a DE problem, then I'd separate the real and complex components of the solution and just like the case when you solve linear DEs, the real and imaginary components are the two real solutions to the DE. Think so anyway.