Integral of $$$\frac{1}{x^{62}}$$$

Find $$$\int \frac{1}{x^{62}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=-62$$$:

$${\color{red}{\int{\frac{1}{x^{62}} d x}}}={\color{red}{\int{x^{-62} d x}}}={\color{red}{\frac{x^{-62 + 1}}{-62 + 1}}}={\color{red}{\left(- \frac{x^{-61}}{61}\right)}}={\color{red}{\left(- \frac{1}{61 x^{61}}\right)}}$$

Therefore,

$$\int{\frac{1}{x^{62}} d x} = - \frac{1}{61 x^{61}}$$

Add the constant of integration:

$$\int{\frac{1}{x^{62}} d x} = - \frac{1}{61 x^{61}}+C$$

$$$\int \frac{1}{x^{62}}\, dx = - \frac{1}{61 x^{61}} + C$$$A