Laplace transform of an expression using transform tables

[PainterGuy]

TL;DR

I was working to find Laplace transform using the table and wanted to know that if my final result is correct

Hi,

I 'm trying to find the Laplace transform of the following expression.

I used the following conversion formulas.
I think "1" is equivalent to unit step function who Laplace transform is 1/s.

I ended up with the following final Laplace transform.

Is my final result correct? Thank you for the help!

 

[DrClaude]

Your Laplace transforms are correct, but not your subsequent algebra. The last term in the first (red) line is where the error appears.

 

[PainterGuy]

The last term in the first (red) line is where the error appears.

I tried to fix the error. Could you please give it a look? For some reason, I think that in the numerator I should only get "10" and not "2s+10".

 

[DrClaude]

You make the same mistake in the numerator, now at the beginning of the second line.

 

[PainterGuy]

You make the same mistake in the numerator, now at the beginning of the second line.

Sorry!

It looks good now.

 

[DrClaude]

Correct!