What is the integral of (x^{1/3})/(x^{2/3)} ?

The integral of (x^{1/3})/(x^{2/3)} is 3/2 x^{2/3}+C

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integral of (x^{1/3})/(x^{2/3)}

\int \frac{x ^{\frac{1}{3}}}{x ^{\frac{2}{3}}} d x

\frac{3}{2} x^{\frac{2}{3}} + C

Solution steps

\int \frac{x ^{\frac{1}{3}}}{x ^{\frac{2}{3}}} d x

Simplify

\frac{x ^{\frac{1}{3}}}{x ^{\frac{2}{3}}} : \frac{1}{x ^{\frac{1}{3}}}

= \int \frac{1}{x ^{\frac{1}{3}}} d x

Apply the Power Rule

: \frac{3}{2} x^{\frac{2}{3}}

= \frac{3}{2} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{2} x^{\frac{2}{3}} + C

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What is the integral of (x^{1/3})/(x^{2/3)} ?
The integral of (x^{1/3})/(x^{2/3)} is 3/2 x^{2/3}+C