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

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

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

\int \frac{1}{x \cdot 3 x} d x

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

Solution steps

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

Simplify

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

= \int \frac{1}{x ^{\frac{4}{3}}} d x

Apply the Power Rule

: - \frac{3}{3 x}

= - \frac{3}{3 x}

Add a constant to the solution

= - \frac{3}{3 x} + C

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What is the integral of 1/(x*\sqrt[3]{x)} ?
The integral of 1/(x*\sqrt[3]{x)} is -3/(\sqrt[3]{x)}+C