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

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

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

integral

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

2^{\frac{1}{3}} \cdot \frac{3}{5} x^{\frac{5}{3}} + C

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Power Rule

= 2^{\frac{1}{3}} \cdot \frac{3}{5} x^{\frac{5}{3}}

Add a constant to the solution

= 2^{\frac{1}{3}} \cdot \frac{3}{5} x^{\frac{5}{3}} + C

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