Inverse Laplace Transform

Could Anyone help me with this problem...
I am stuck at the inverting..


Please Look at the attached file..

Hi !

There is a mistake (see attachment). I didn't verify the equations following the mistaken equation.

Ok..I corrected it... it made me end up with an fraction
http://snag.gy/bLvpm.jpg

But how do i Perform the inverse laplace transform on this fraction..

Look below :

Mathmatica says it is false.... .... ......

http://snag.gy/PP3nE.jpg

Why not doing it by hand ?
No need for a computer to do such a simple calculus !

Using a computer requires a non ambiguous writing !