Integral of $$$\frac{1}{s^{2}}$$$

Find $$$\int \frac{1}{s^{2}}\, ds$$$.

Apply the power rule $$$\int s^{n}\, ds = \frac{s^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=-2$$$:

$${\color{red}{\int{\frac{1}{s^{2}} d s}}}={\color{red}{\int{s^{-2} d s}}}={\color{red}{\frac{s^{-2 + 1}}{-2 + 1}}}={\color{red}{\left(- s^{-1}\right)}}={\color{red}{\left(- \frac{1}{s}\right)}}$$

Therefore,

$$\int{\frac{1}{s^{2}} d s} = - \frac{1}{s}$$

Add the constant of integration:

$$\int{\frac{1}{s^{2}} d s} = - \frac{1}{s}+C$$

$$$\int \frac{1}{s^{2}}\, ds = - \frac{1}{s} + C$$$A