What is the integral of \sqrt[4]{x^2} ?

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

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integral of \sqrt[4]{x^2}

\int 4 x^{2} d x

\frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int 4 x^{2} d x

4 x^{2} = x,

assuming

x \geq 0

= \int x d x

Apply the Power Rule

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

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + C

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