Integral de $$$\frac{1}{\sqrt[21]{y}}$$$

Encontre $$$\int \frac{1}{\sqrt[21]{y}}\, dy$$$.

Aplique a regra da potência $$$\int y^{n}\, dy = \frac{y^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=- \frac{1}{21}$$$:

$${\color{red}{\int{\frac{1}{\sqrt[21]{y}} d y}}}={\color{red}{\int{y^{- \frac{1}{21}} d y}}}={\color{red}{\frac{y^{- \frac{1}{21} + 1}}{- \frac{1}{21} + 1}}}={\color{red}{\left(\frac{21 y^{\frac{20}{21}}}{20}\right)}}$$

Portanto,

$$\int{\frac{1}{\sqrt[21]{y}} d y} = \frac{21 y^{\frac{20}{21}}}{20}$$

Adicione a constante de integração:

$$\int{\frac{1}{\sqrt[21]{y}} d y} = \frac{21 y^{\frac{20}{21}}}{20}+C$$

$$$\int \frac{1}{\sqrt[21]{y}}\, dy = \frac{21 y^{\frac{20}{21}}}{20} + C$$$A