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

The integral of x/(\sqrt[3]{5x^2)} is 3/(4\sqrt[3]{5)}x^{4/3}+C

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

Simplify

\frac{x}{x ^{\frac{2}{3}}} : x^{\frac{1}{3}}

Apply the Power Rule

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

Simplify

Add a constant to the solution

\int sin (2 x) e^{3 x} d x

\int 24 x^{5} arccot (2 x^{3}) d x

\int \frac{1}{x ^{2} ( x ^{2} + 4 )} d x

\int \frac{x ^{3} + 1}{x ^{3} + x} d x

What is the integral of x/(\sqrt[3]{5x^2)} ?
The integral of x/(\sqrt[3]{5x^2)} is 3/(4\sqrt[3]{5)}x^{4/3}+C