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

Find $$$\int x^{- a}\, dx$$$.

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

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

Therefore,

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

Simplify:

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

Add the constant of integration:

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

$$$\int x^{- a}\, dx = - \frac{x^{1 - a}}{a - 1} + C$$$A