Example 03 | The General Power Formula

$\displaystyle \int \dfrac{dx}{\sqrt[7]{x^2}}$

$= \displaystyle \int \dfrac{dx}{x^{2/7}}$

$= \displaystyle \int x^{-2/7} \, dx$

$= \dfrac{x^{5/7}}{5/7} + C$

$= \frac{7}{5}x^{5/7} + C$

$= \frac{7}{5}\sqrt[7]{x^5} + C$           answer