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Re: Tough Limit

Well, I guessed I missed sth.
Additionally, you have to assume a real omega:

Integrate[Sin[\[Omega]*t]*Exp[(-t)*s], {t, 0, Infinity},
  Assumptions -> Inequality[s, Greater, 0, Equal, Im[\[Omega]]]]

or - because you'll get s^2+omega^2 in the denominator:

Integrate[Sin[\[Omega]*t]/E^(t*s), {t, 0, Infinity},
  Assumptions -> s > Abs[Im[\[Omega]]]]


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