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

The integral of 1/(x\sqrt[3]{x^2)} is -3/(2x^{2/3)}+C

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integral of 1/(x\sqrt[3]{x^2)}

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

Solution steps

assuming

x \geq 0

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

Simplify

\frac{1}{x x ^{\frac{2}{3}}} : \frac{1}{x ^{\frac{5}{3}}}

= \int \frac{1}{x ^{\frac{5}{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 1/(x\sqrt[3]{x^2)} ?
The integral of 1/(x\sqrt[3]{x^2)} is -3/(2x^{2/3)}+C