Calculus Level 4

$\large \large \int _{-\infty }^{\infty } 3\mathcal{L}^{-1} \left[\:\sum _{k=0}^{\infty }\:\:2s^k\:+\:5\sum _{k=1}^{\infty }\:\:ks^k\:\right]\:dt = \ ?$

Note: $$\mathcal{L}$$ denotes the Laplace Transformation operator.

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