Open Question: What is the inverse Laplace transform of s/ s^2 +4s +5?

Open Question: What is the inverse Laplace transform of s/ s^2 +4s +5?

Explain how they got the correct answer: e^-2t cost -2e^-2t sint

I get e^-2t cost t but I don't know how to obtain -2e^-2t sint.

What technique is used here. And explain WHY.

I saw the solutions manual and I don't understand what gets done at the numerator.


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