Integral of $$$\frac{1}{x^{29}}$$$

Find $$$\int \frac{1}{x^{29}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=-29$$$:

$${\color{red}{\int{\frac{1}{x^{29}} d x}}}={\color{red}{\int{x^{-29} d x}}}={\color{red}{\frac{x^{-29 + 1}}{-29 + 1}}}={\color{red}{\left(- \frac{x^{-28}}{28}\right)}}={\color{red}{\left(- \frac{1}{28 x^{28}}\right)}}$$

Therefore,

$$\int{\frac{1}{x^{29}} d x} = - \frac{1}{28 x^{28}}$$

Add the constant of integration:

$$\int{\frac{1}{x^{29}} d x} = - \frac{1}{28 x^{28}}+C$$

$$$\int \frac{1}{x^{29}}\, dx = - \frac{1}{28 x^{28}} + C$$$A