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

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

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

\frac{1}{2} x^{\frac{2}{3}} + C

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply the Power Rule

= \frac{1}{3} \cdot \frac{3}{2} x^{\frac{2}{3}}

Simplify

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

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

Add a constant to the solution

= \frac{1}{2} x^{\frac{2}{3}} + C

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