How do I find the inverse laplace transform of this?

[Abhishekdas]

What I've tried:

But, the integration will be too long with this method. Is there any easier and faster method to solve this?

 

[HallsofIvy]

You don't typically integrate to find an inverse Laplace transform, you look it up in a table. And it looks like you have already done that! You are finished- there is no "integration" or other work to be done!