What is the integral of 1/(3\sqrt[3]{x^2)} ?

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

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integral of 1/(3\sqrt[3]{x^2)}

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

Apply the Power Rule

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

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

Simplify

Add a constant to the solution

y = \frac{x ^{2} - 1}{x ^{2} + x + 1}

\frac{d}{d x} (s e^{s x})

y^{^{'}} = y + y^{3}

y^{^{'}} = 7 y x^{5}

y^{^{'}} = \frac{e ^{y}}{x ^{3}}

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