Integral de $$$\frac{1}{x^{\frac{2}{3}}}$$$

Halla $$$\int \frac{1}{x^{\frac{2}{3}}}\, dx$$$.

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=- \frac{2}{3}$$$:

$${\color{red}{\int{\frac{1}{x^{\frac{2}{3}}} d x}}}={\color{red}{\int{x^{- \frac{2}{3}} d x}}}={\color{red}{\frac{x^{- \frac{2}{3} + 1}}{- \frac{2}{3} + 1}}}={\color{red}{\left(3 x^{\frac{1}{3}}\right)}}={\color{red}{\left(3 \sqrt[3]{x}\right)}}$$

Por lo tanto,

$$\int{\frac{1}{x^{\frac{2}{3}}} d x} = 3 \sqrt[3]{x}$$

Añade la constante de integración:

$$\int{\frac{1}{x^{\frac{2}{3}}} d x} = 3 \sqrt[3]{x}+C$$

$$$\int \frac{1}{x^{\frac{2}{3}}}\, dx = 3 \sqrt[3]{x} + C$$$A