Integral de $$$\frac{1}{x^{9}}$$$

Halla $$$\int \frac{1}{x^{9}}\, dx$$$.

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=-9$$$:

$${\color{red}{\int{\frac{1}{x^{9}} d x}}}={\color{red}{\int{x^{-9} d x}}}={\color{red}{\frac{x^{-9 + 1}}{-9 + 1}}}={\color{red}{\left(- \frac{x^{-8}}{8}\right)}}={\color{red}{\left(- \frac{1}{8 x^{8}}\right)}}$$

Por lo tanto,

$$\int{\frac{1}{x^{9}} d x} = - \frac{1}{8 x^{8}}$$

Añade la constante de integración:

$$\int{\frac{1}{x^{9}} d x} = - \frac{1}{8 x^{8}}+C$$

$$$\int \frac{1}{x^{9}}\, dx = - \frac{1}{8 x^{8}} + C$$$A