Laplace Transform Help: Solving Equation (1)

AI Thread Summary
The discussion focuses on how to apply the Laplace transform to a specific equation, with users seeking clarity on the transformation process. The correct solution is known, but the method to derive it remains unclear, particularly regarding the integration from t0 to 0 and from 0 to t. A key point mentioned is that the Laplace transform of an integral from 0 to t results in X(s)/s. The challenge lies in understanding the derivation of the "left-over term" in the solution. Overall, participants are collaborating to clarify the steps involved in obtaining the correct Laplace transform.
MHR-Love
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Hi guys,

Would you help me in finding how Laplace transform is done for equation (1) in the attached image?
Equation (2) is the correct solution but I don't know how we get it!
I know that we can split the integration in (1) into two parts; one is from t0 to 0 and the other part is from 0 to t, but i couldn't find it Laplace transform too.

Thank you
 

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wikipedia's article for Laplace transforms will show you that the transform of an integral of x(t') from 0 to t gives X(s)/s. Use this rule to get term 1 in eq2. term 2 is the left-over bit, and term 3 is the transform of a constant which is the constant*1/s
 
thnx guys for replying. My problem is actually with that left-over term which I don't know how we get!
 

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