Integral of $$$a^{- n}$$$ with respect to $$$a$$$

Find $$$\int a^{- n}\, da$$$.

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

$${\color{red}{\int{a^{- n} d a}}}={\color{red}{\frac{a^{1 - n}}{1 - n}}}={\color{red}{\frac{a^{1 - n}}{1 - n}}}$$

Therefore,

$$\int{a^{- n} d a} = \frac{a^{1 - n}}{1 - n}$$

Simplify:

$$\int{a^{- n} d a} = - \frac{a^{1 - n}}{n - 1}$$

Add the constant of integration:

$$\int{a^{- n} d a} = - \frac{a^{1 - n}}{n - 1}+C$$

$$$\int a^{- n}\, da = - \frac{a^{1 - n}}{n - 1} + C$$$A