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July 1st, 2017, 05:26 PM  #1 
Newbie Joined: Jun 2017 From: N/A Posts: 4 Thanks: 0  Laplace transform
I don't know how the transform was determined from the solution that the book gave. 
July 1st, 2017, 07:25 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,597 Thanks: 546 Math Focus: Yet to find out. 
There may be a quicker way with some tricky substitution or something, but i haven't looked at it for very long. But you can just work through the algebra for this. You will end up with a bunch of similar terms which will likely factor out and result in the above equation. Nothing new here that i can see. 
July 3rd, 2017, 08:18 PM  #3 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 622 Thanks: 87 Math Focus: Electrical Engineering Applications 
Hi bdewbac, I worked the problem using the delay ($t$ shift) property of the Laplace Transform: $\displaystyle \large f(tt_0) \ u(tt_0) \Leftrightarrow e^{st_0}F(s)$ Since: $\displaystyle \large t \ u(t) \Leftrightarrow \frac{1}{s^2}$ Then, for example: $\displaystyle \large 10 \ (t2) \ u(t2) \Leftrightarrow 10 \frac{e^{2s}}{s^2}$ I hope that this helps. 

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