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

The integral of \sqrt[5]{x^3} is 5/8 x^{8/5}+C

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integral of \sqrt[5]{x^3}

\int 5 x^{3} d x

\frac{5}{8} x^{\frac{8}{5}} + C

Solution steps

\int 5 x^{3} d x

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

assuming

x \geq 0

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

Apply the Power Rule

: \frac{5}{8} x^{\frac{8}{5}}

= \frac{5}{8} x^{\frac{8}{5}}

Add a constant to the solution

= \frac{5}{8} x^{\frac{8}{5}} + C

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What is the integral of \sqrt[5]{x^3} ?
The integral of \sqrt[5]{x^3} is 5/8 x^{8/5}+C