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

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

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

\int (4 3 x) d x

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

Solution steps

\int 4 3 x d x

Take the constant out:

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

= 4 \cdot \int 3 x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

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