Integral of $$$\frac{1}{x^{11}}$$$

Find $$$\int \frac{1}{x^{11}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=-11$$$:

$${\color{red}{\int{\frac{1}{x^{11}} d x}}}={\color{red}{\int{x^{-11} d x}}}={\color{red}{\frac{x^{-11 + 1}}{-11 + 1}}}={\color{red}{\left(- \frac{x^{-10}}{10}\right)}}={\color{red}{\left(- \frac{1}{10 x^{10}}\right)}}$$

Therefore,

$$\int{\frac{1}{x^{11}} d x} = - \frac{1}{10 x^{10}}$$

Add the constant of integration:

$$\int{\frac{1}{x^{11}} d x} = - \frac{1}{10 x^{10}}+C$$

$$$\int \frac{1}{x^{11}}\, dx = - \frac{1}{10 x^{10}} + C$$$A