What is the integral of x/(\sqrt[3]{x^2)} ?

The integral of x/(\sqrt[3]{x^2)} is 3/4 x^{4/3}+C

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integral of x/(\sqrt[3]{x^2)}

\frac{3}{4} x^{\frac{4}{3}} + C

Solution steps

assuming

x \geq 0

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

Simplify

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

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

Apply the Power Rule

: \frac{3}{4} x^{\frac{4}{3}}

= \frac{3}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} + C

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What is the integral of x/(\sqrt[3]{x^2)} ?
The integral of x/(\sqrt[3]{x^2)} is 3/4 x^{4/3}+C