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

Find $$$\int t^{- n}\, dt$$$.

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

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

Therefore,

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

Simplify:

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

Add the constant of integration:

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

$$$\int t^{- n}\, dt = - \frac{t^{1 - n}}{n - 1} + C$$$A