Integral of $$$\frac{1}{x^{6}}$$$

Find $$$\int \frac{1}{x^{6}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=-6$$$:

$${\color{red}{\int{\frac{1}{x^{6}} d x}}}={\color{red}{\int{x^{-6} d x}}}={\color{red}{\frac{x^{-6 + 1}}{-6 + 1}}}={\color{red}{\left(- \frac{x^{-5}}{5}\right)}}={\color{red}{\left(- \frac{1}{5 x^{5}}\right)}}$$

Therefore,

$$\int{\frac{1}{x^{6}} d x} = - \frac{1}{5 x^{5}}$$

Add the constant of integration:

$$\int{\frac{1}{x^{6}} d x} = - \frac{1}{5 x^{5}}+C$$

$$$\int \frac{1}{x^{6}}\, dx = - \frac{1}{5 x^{5}} + C$$$A