What is the integral of \sqrt[3]{xsqrt(x)} ?

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

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integral of \sqrt[3]{xsqrt(x)}

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

Solution steps

Apply exponent rule:

(a \cdot b)^{n} = a^{n} \cdot b^{n}

assuming

x \geq 0

Simplify

= \int x d x

Apply the Power Rule

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

= \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[3]{xsqrt(x)} ?
The integral of \sqrt[3]{xsqrt(x)} is 2/3 x^{3/2}+C