- #1

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g(t)=t^2 * sin(3t) * x(t) where x(t) has an already defined laplace transform.

do you actually include x(t) in your laplace transformation? Because when I see other problems that have u(t) at the end you don't really do anything with them, you only worry about the terms in front of it. Like f(t)=sin(3t)u(t), the answer is simply 3 / (s^2 + 9)....u(t) is not included in it.