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

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

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integral of 5/(3\sqrt[3]{x^2)}

\int \frac{5}{3 3 x ^{2}} d x

5 3 x + C

Solution steps

\int \frac{5}{3 3 x ^{2}} d x

Take the constant out:

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

= \frac{5}{3} \cdot \int \frac{1}{3 x ^{2}} d x

3 x^{2} = x^{\frac{2}{3}},

assuming

x \geq 0

= \frac{5}{3} \cdot \int \frac{1}{x ^{\frac{2}{3}}} d x

Apply the Power Rule

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

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

Simplify

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

= 5 3 x

Add a constant to the solution

= 5 3 x + C

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