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