Integral of $$$\frac{1}{x^{81}}$$$

Find $$$\int \frac{1}{x^{81}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=-81$$$:

$${\color{red}{\int{\frac{1}{x^{81}} d x}}}={\color{red}{\int{x^{-81} d x}}}={\color{red}{\frac{x^{-81 + 1}}{-81 + 1}}}={\color{red}{\left(- \frac{x^{-80}}{80}\right)}}={\color{red}{\left(- \frac{1}{80 x^{80}}\right)}}$$

Therefore,

$$\int{\frac{1}{x^{81}} d x} = - \frac{1}{80 x^{80}}$$

Add the constant of integration:

$$\int{\frac{1}{x^{81}} d x} = - \frac{1}{80 x^{80}}+C$$

$$$\int \frac{1}{x^{81}}\, dx = - \frac{1}{80 x^{80}} + C$$$A