About evaluating $\mathcal{L}^{-1}_{s\to x}\bigl\{\frac{F(s)}{s}\bigr\}$ by considering contour integration with different entire functions $F(s)$

Question

Detailedly compare the difficulties of different entire functions $F(s)$ where $F(0)\neq0$ when evaluating $\mathcal{L}^{-1}_{s\to x}\bigl\{\frac{F(s)}{s}\bigr\}$ by considering contour integration, e.g. $\mathcal{L}^{-1}_{s\to x}\bigl\{\frac{1}{s}\bigr\}$ , $\mathcal{L}^{-1}_{s\to x}\bigl\{\frac{e^{as}}{s}\bigr\}$ , $\mathcal{L}^{-1}_{s\to x}\bigl\{\frac{e^{as^2+bs}}{s}\bigr\}$ and $\mathcal{L}^{-1}_{s\to x}\left\{\frac{\cos as}{s}\right\}$ , where $a$ and $b$ are real numbers and $a\neq0$ .