Integral of $$$x^{1 - n}$$$ with respect to $$$x$$$

Find $$$\int x^{1 - n}\, dx$$$.

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

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

Therefore,

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

Simplify:

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

Add the constant of integration:

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

$$$\int x^{1 - n}\, dx = - \frac{x^{2 - n}}{n - 2} + C$$$A