What is the integral of (\sqrt[3]{x^2})/(12) ?

The integral of (\sqrt[3]{x^2})/(12) is 1/20 x^{5/3}+C

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integral of (\sqrt[3]{x^2})/(12)

\frac{1}{20} x^{\frac{5}{3}} + C

Solution steps

Take the constant out:

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

assuming

x \geq 0

= \frac{1}{12} \cdot \int x^{\frac{2}{3}} d x

Apply the Power Rule

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

= \frac{1}{12} \cdot \frac{3}{5} x^{\frac{5}{3}}

Simplify

\frac{1}{12} \cdot \frac{3}{5} x^{\frac{5}{3}} : \frac{1}{20} x^{\frac{5}{3}}

= \frac{1}{20} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{1}{20} x^{\frac{5}{3}} + C

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What is the integral of (\sqrt[3]{x^2})/(12) ?
The integral of (\sqrt[3]{x^2})/(12) is 1/20 x^{5/3}+C