Integral of $$$\frac{x^{a}}{x^{2}}$$$ with respect to $$$x$$$

Find $$$\int \frac{x^{a}}{x^{2}}\, dx$$$.

The input is rewritten: $$$\int{\frac{x^{a}}{x^{2}} d x}=\int{x^{a - 2} d x}$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=a - 2$$$:

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

Therefore,

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

Add the constant of integration:

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

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