Integrale di $$$\frac{1}{\sqrt[21]{y}}$$$

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

Applica la regola della potenza $$$\int y^{n}\, dy = \frac{y^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=- \frac{1}{21}$$$:

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

Pertanto,

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

Aggiungi la costante di integrazione:

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

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