Transform, Add, Integrate. Large?

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.