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Integral de $$$\frac{1}{\sqrt[6]{x}}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{1}{\sqrt[6]{x}}\, dx$$$.
Solución
Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=- \frac{1}{6}$$$:
$${\color{red}{\int{\frac{1}{\sqrt[6]{x}} d x}}}={\color{red}{\int{x^{- \frac{1}{6}} d x}}}={\color{red}{\frac{x^{- \frac{1}{6} + 1}}{- \frac{1}{6} + 1}}}={\color{red}{\left(\frac{6 x^{\frac{5}{6}}}{5}\right)}}$$
Por lo tanto,
$$\int{\frac{1}{\sqrt[6]{x}} d x} = \frac{6 x^{\frac{5}{6}}}{5}$$
Añade la constante de integración:
$$\int{\frac{1}{\sqrt[6]{x}} d x} = \frac{6 x^{\frac{5}{6}}}{5}+C$$
Respuesta
$$$\int \frac{1}{\sqrt[6]{x}}\, dx = \frac{6 x^{\frac{5}{6}}}{5} + C$$$A