Need help with Laplace transforms

[blah]

Does anyone have an elegant way to show the following:

I found this after almost an hour of messing around My solution isn't nice at all. I was wondering if anyone else could come up with something that doesn't involve working backwards. Or is there another inverse that's more elegant than this?

On a side note, does anyone know of any good websites/programs that can convert LaTeX to images quickly?

 

[Lucas Garron]

On a side note, does anyone know of any good websites/programs that can convert LaTeX to images quickly?

LaTeXiT, on Mac

If only I'd have learned more about Laplace transforms to actually know what I'm doing and help you...

 

[blah]

On a side note, does anyone know of any good websites/programs that can convert LaTeX to images quickly?

LaTeXiT

on Mac

 

[Karthik]

Split the fraction like this

Then use Heaviside partial fractions to split the second term like this

I think A=-0.25, B=-0.25, C=0.25, D=-0.25

Now use the standard Inverse Laplace transforms and the derivative property to solve it.

Here is a web-tool to convert latex equations to images: http://www.equationsheet.com/textoimage.php

Edit: BTW j=sqrt(-1). Many people use 'i' though.