Laplace Transform Help: Solving Equation (1)

[MHR-Love]

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

 

[Greg-ulate]

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

 

[MHR-Love]

thnx guys for replying. My problem is actually with that left-over term which I don't know how we get!