Inverse Laplace Transform of the following complicated form

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What would be the inverse laplace transform of the following:

I mean I want to solve this:

$$ \large \mathcal {L^{-1} [ \mathcal {L}[{sin(at+b)}] . \mathcal{L} [{e^{xt}}] . e^{cs}}] = ? $$

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Brut force calculus : First, we introduce the Laplace transforms of the given functions. Second, we separate the fractions. Third, we apply the inverse Laplace transform.

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