What is the integral of (30)/(\sqrt[3]{x^2)} ?

The integral of (30)/(\sqrt[3]{x^2)} is 90\sqrt[3]{x}+C

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integral of (30)/(\sqrt[3]{x^2)}

\int \frac{30}{3 x ^{2}} d x

90 3 x + C

Solution steps

\int \frac{30}{3 x ^{2}} d x

Take the constant out:

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

= 30 \cdot \int \frac{1}{3 x ^{2}} d x

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

assuming

x \geq 0

= 30 \cdot \int \frac{1}{x ^{\frac{2}{3}}} d x

Apply the Power Rule

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

= 30 \cdot 3 x^{\frac{1}{3}}

Simplify

30 \cdot 3 x^{\frac{1}{3}} : 90 3 x

= 90 3 x

Add a constant to the solution

= 90 3 x + C

\frac{d}{d x} (\frac{x ^{2} - 3}{x})

\int \frac{5 t ^{2}}{2} d t

\int \frac{300}{2 q + 25} d q

x \to - 5 lim (10 x + 3)

\frac{d}{d x} (4 x - sin (2 x))

What is the integral of (30)/(\sqrt[3]{x^2)} ?
The integral of (30)/(\sqrt[3]{x^2)} is 90\sqrt[3]{x}+C