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I am trying to figure out in my notes how my professor did

L[(e^-3t)(sin2t)] = 2/(s+3)^2 +4

I think she just did it in her head and wrote it, so I don't actually know how to solve it. I am looking at my table of laplace transforms and there is none for a product of an exponential and sin/cos.

I tried solving this with the definition, and I came across a integration by parts that looks particularly nasty, not even sure if solvable.

Anyways, can anyone point me in the right direction to this one? I know the product of a laplace transforms is not the laplace of the products, so thats out.

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# Laplace Transform of the product of two functions

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