Problem with Laplace transform

[JMB]

I guess that by U(t) you mean the step function. In that case you need to use the HP Prime function Heaviside().

The step function at t=0 is Heaviside(t), and the step function at other values, say t=2, is Heaviside(t-2).

Using this function you get:

laplace(Heaviside(t),t,p) = 1/p

laplace(Heaviside(t-2),t,p) = e^(-2*p)/p

laplace(Heaviside(t)+(t-2)^2*Heavisede(t-2),t,p) = (p^2+2*e^(-2*p)) / p^3