I am in the middle of solving a integro-differential, and I need to use inverse Laplace transforms to complete the last bit, I have the following:

I have simplified this to the following form:

Then using partial fractions I have taken the above term by term, and done the following:

Second term:

Can some please varify if I have used partial fractions correctly on the first 2 expressions

Also I do not understand how to use partial fraction on the third expression, can some please help and explain how I would do this... ?