What is the integral of 2/(3\sqrt[6]{x)} ?

The integral of 2/(3\sqrt[6]{x)} is 4/5 x^{5/6}+C

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integral of 2/(3\sqrt[6]{x)}

\int \frac{2}{3 6 x} d x

\frac{4}{5} x^{\frac{5}{6}} + C

Solution steps

\int \frac{2}{3 6 x} d x

Take the constant out:

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

= \frac{2}{3} \cdot \int \frac{1}{6 x} d x

Apply the Power Rule

: \frac{6}{5} x^{\frac{5}{6}}

= \frac{2}{3} \cdot \frac{6}{5} x^{\frac{5}{6}}

Simplify

\frac{2}{3} \cdot \frac{6}{5} x^{\frac{5}{6}} : \frac{4}{5} x^{\frac{5}{6}}

= \frac{4}{5} x^{\frac{5}{6}}

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{6}} + C

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What is the integral of 2/(3\sqrt[6]{x)} ?
The integral of 2/(3\sqrt[6]{x)} is 4/5 x^{5/6}+C