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

The integral of (\sqrt[3]{x})/3 is 1/4 x^{4/3}+C

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

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

\frac{1}{4} x^{\frac{4}{3}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= \frac{1}{3} \cdot \frac{3}{4} x^{\frac{4}{3}}

Simplify

\frac{1}{3} \cdot \frac{3}{4} x^{\frac{4}{3}} : \frac{1}{4} x^{\frac{4}{3}}

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

Add a constant to the solution

= \frac{1}{4} x^{\frac{4}{3}} + C

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What is the integral of (\sqrt[3]{x})/3 ?
The integral of (\sqrt[3]{x})/3 is 1/4 x^{4/3}+C