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I'm trying to find the inverse laplace transform of the following function:

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The resulting inverse laplace is in the form:

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Not sure where the derivatives came from, or what the inverse laplace of a polynomial is, as I couldn't find it on LT table.

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Multiplication by $s$ in the Laplace domain corresponds to differentiation in time. Thus, $f^{(n)}(t) \iff s^n F(s)$.

Similarly, division by $s$ in the Laplace domain corresponds to integration in time.

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