What is the integral of (\sqrt[11]{x^{10}}) ?

The integral of (\sqrt[11]{x^{10}}) is 11/21 x^{21/11}+C

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integral of (\sqrt[11]{x^{10}})

\int (11 x^{10}) d x

\frac{11}{21} x^{\frac{21}{11}} + C

Solution steps

\int 11 x^{10} d x

11 x^{10} = x^{\frac{10}{11}},

assuming

x \geq 0

= \int x^{\frac{10}{11}} d x

Apply the Power Rule

: \frac{11}{21} x^{\frac{21}{11}}

= \frac{11}{21} x^{\frac{21}{11}}

Add a constant to the solution

= \frac{11}{21} x^{\frac{21}{11}} + C

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What is the integral of (\sqrt[11]{x^{10}}) ?
The integral of (\sqrt[11]{x^{10}}) is 11/21 x^{21/11}+C