Bear with me here, I took DIFF EQ 3 semesters ago and laplace transforms have come up again in a new class and I need to help

Solve the following using Laplace transforms:

where x and

I get the equation down to

then

next I went to partial fractions:

then finding a common denominator and setting it equal to 1 i get

Solving that I get and

Plugging these back in I get

Now this is where I am stuck....I my table I cannot find a tranfer related to and I do not know how to manipulate it so I can use the tables.