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Find $\mathcal{L}^{-1}\left(F(s)\right)$ if:

$$\displaystyle F(s) = \frac{1+2s}{s^3}$$

A

$$\frac{t^2}{2} - t$$

B

$$\frac{t^2}{2} + 2t$$

C

$$\frac{3t^2}{2} + t$$

D

$$\frac{5t^2}{2} - \frac{1}{2}t$$

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