What is the integral of \sqrt[5]{r^2} ?

The integral of \sqrt[5]{r^2} is 5/7 r^{7/5}+C

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integral of \sqrt[5]{r^2}

\int 5 r^{2} d r

\frac{5}{7} r^{\frac{7}{5}} + C

Solution steps

\int 5 r^{2} d r

5 r^{2} = r^{\frac{2}{5}},

assuming

r \geq 0

= \int r^{\frac{2}{5}} d r

Apply the Power Rule

: \frac{5}{7} r^{\frac{7}{5}}

= \frac{5}{7} r^{\frac{7}{5}}

Add a constant to the solution

= \frac{5}{7} r^{\frac{7}{5}} + C

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What is the integral of \sqrt[5]{r^2} ?
The integral of \sqrt[5]{r^2} is 5/7 r^{7/5}+C