What is the integral of (-4)/(\sqrt[3]{x^2)} ?

The integral of (-4)/(\sqrt[3]{x^2)} is -12\sqrt[3]{x}+C

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integral of (-4)/(\sqrt[3]{x^2)}

\int \frac{- 4}{3 x ^{2}} d x

- 12 3 x + C

Solution steps

\int \frac{- 4}{3 x ^{2}} d x

Take the constant out:

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

= - 4 \cdot \int \frac{1}{3 x ^{2}} d x

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

assuming

x \geq 0

= - 4 \cdot \int \frac{1}{x ^{\frac{2}{3}}} d x

Apply the Power Rule

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

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

Simplify

- 4 \cdot 3 x^{\frac{1}{3}} : - 12 3 x

= - 12 3 x

Add a constant to the solution

= - 12 3 x + C

x \to 3 lim (\frac{x - 1}{3 - x})

x^{y} + 1

f (x) = e^{2 x} - x^{2} - 1

ln (x^{7})

\int_{0}^{4} x^{3} d x

What is the integral of (-4)/(\sqrt[3]{x^2)} ?
The integral of (-4)/(\sqrt[3]{x^2)} is -12\sqrt[3]{x}+C