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

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

The input is rewritten: $$$\int{\frac{x^{n}}{x} d x}=\int{x^{n - 1} d x}$$$.

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

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

Therefore,

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

Add the constant of integration:

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

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