Indefinite Integration of 1/(3√x^2): Solving for x

[draotic]

Homework Statement

1 / (³√x² )

Homework Equations

The Attempt at a Solution

the overall power of x in denom becomes ( 1/2 * 2 * 1/3 = 1/3)
taking in num , it becomes (-1/3 + 1 = 2/3) so answer should be x^2/3 / (2/3)
which is wrong , please help

 

[SammyS]

Homework Statement

1 / (³√x² )

Homework Equations

The Attempt at a Solution

the overall power of x in denom becomes ( 1/2 * 2 * 1/3 = 1/3)
taking in num , it becomes (-1/3 + 1 = 2/3) so answer should be x^2/3 / (2/3)
which is wrong , please help

$\displaystyle \frac{1}{\sqrt[3]{x^2}\,}=\frac{1}{x^{2/3}}=x^{-2/3}$

$\displaystyle -\frac{2}{3}+1=\frac{1}{3}$