Yeah it was something like that, it's been a couple of years since I've taken signals and systems but that looks about right. You've got to use the fact that a translation in frequency a is a multiplication in time by exp(at). You can also use the fact that integrating in time is the same as multiplying by 1/jw in frequency.
So you start out with an f(t) = 1 => F(w) = delta(t)
then integrate twice to get g(t) = t*u(t) => G(w)=1/(jw^2)
and then take the frequency domain translation by 5 and you get h(t) = exp(-5t)*t*u(t) => H(w) = 1/(jw+5)^2
Done like dinner.
So you start out with an f(t) = 1 => F(w) = delta(t)
then integrate twice to get g(t) = t*u(t) => G(w)=1/(jw^2)
and then take the frequency domain translation by 5 and you get h(t) = exp(-5t)*t*u(t) => H(w) = 1/(jw+5)^2
Done like dinner.
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