What is the integral of (\sqrt[3]{x^{11}}) ?

The integral of (\sqrt[3]{x^{11}}) is 3/14 x^{14/3}+C

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integral of (\sqrt[3]{x^{11}})

\int (3 x^{11}) d x

\frac{3}{14} x^{\frac{14}{3}} + C

Solution steps

\int 3 x^{11} d x

3 x^{11} = x^{\frac{11}{3}},

assuming

x \geq 0

= \int x^{\frac{11}{3}} d x

Apply the Power Rule

: \frac{3}{14} x^{\frac{14}{3}}

= \frac{3}{14} x^{\frac{14}{3}}

Add a constant to the solution

= \frac{3}{14} x^{\frac{14}{3}} + C

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What is the integral of (\sqrt[3]{x^{11}}) ?
The integral of (\sqrt[3]{x^{11}}) is 3/14 x^{14/3}+C