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

The integral of 1/(3\sqrt[4]{x)} is 4/9 x^{3/4}+C

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integral of 1/(3\sqrt[4]{x)}

\frac{4}{9} x^{\frac{3}{4}} + 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{4}{3} x^{\frac{3}{4}}

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

Simplify

\frac{1}{3} \cdot \frac{4}{3} x^{\frac{3}{4}} : \frac{4}{9} x^{\frac{3}{4}}

= \frac{4}{9} x^{\frac{3}{4}}

Add a constant to the solution

= \frac{4}{9} x^{\frac{3}{4}} + C

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What is the integral of 1/(3\sqrt[4]{x)} ?
The integral of 1/(3\sqrt[4]{x)} is 4/9 x^{3/4}+C