Integral of $$$\frac{1}{x^{5}}$$$

Find $$$\int \frac{1}{x^{5}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=-5$$$:

$${\color{red}{\int{\frac{1}{x^{5}} d x}}}={\color{red}{\int{x^{-5} d x}}}={\color{red}{\frac{x^{-5 + 1}}{-5 + 1}}}={\color{red}{\left(- \frac{x^{-4}}{4}\right)}}={\color{red}{\left(- \frac{1}{4 x^{4}}\right)}}$$

Therefore,

$$\int{\frac{1}{x^{5}} d x} = - \frac{1}{4 x^{4}}$$

Add the constant of integration:

$$\int{\frac{1}{x^{5}} d x} = - \frac{1}{4 x^{4}}+C$$

$$$\int \frac{1}{x^{5}}\, dx = - \frac{1}{4 x^{4}} + C$$$A