How to Transform a Piecewise Function Using the Second Shift Theorem?

[robmass]

questions asks to write the piecewise function as a unit step function and then to find the laplace transform

t(e^t) 0≤t≤5
0 t≥3

I know it should be along the lines of

t(e^t) - t(e^t)u(t-5)

which then goes to

t(e^t) - (t-5)(e^(t-5))u(t-5)

I know there should be more to the above equation but I just can't figure out what to do from here

 

[Ray Vickson]

questions asks to write the piecewise function as a unit step function and then to find the laplace transform

t(e^t) 0≤t≤5
0 t≥3

I know it should be along the lines of

t(e^t) - t(e^t)u(t-5)

which then goes to

t(e^t) - (t-5)(e^(t-5))u(t-5)

I know there should be more to the above equation but I just can't figure out what to do from here

Your second equation is wrong: you do not get simply (t-5)(e^(t-5))u(t-5). Work everything out carefully, step-by-step.