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

The integral of (x^2)^{1/3} is 3/5 x^{5/3}+C

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integral of (x^2)^{1/3}

\int (x^{2})^{\frac{1}{3}} d x

\frac{3}{5} x^{\frac{5}{3}} + C

Solution steps

\int (x^{2})^{\frac{1}{3}} d x

(x^{2})^{\frac{1}{3}} = x^{\frac{2}{3}},

assuming

x \geq 0

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

Apply the Power Rule

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

Add a constant to the solution

= \frac{3}{5} x^{\frac{5}{3}} + C

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What is the integral of (x^2)^{1/3} ?
The integral of (x^2)^{1/3} is 3/5 x^{5/3}+C