What is the integral of \sqrt[n]{x} ?

The integral of \sqrt[n]{x} is (nx^{(1+n)/n})/(1+n)+C

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integral of \sqrt[n]{x}

\frac{n x ^{\frac{1 + n}{n}}}{1 + n} + C

Solution steps

Apply the Power Rule

: \frac{n x ^{\frac{1 + n}{n}}}{1 + n}

= \frac{n x ^{\frac{1 + n}{n}}}{1 + n}

Add a constant to the solution

= \frac{n x ^{\frac{1 + n}{n}}}{1 + n} + C

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What is the integral of \sqrt[n]{x} ?
The integral of \sqrt[n]{x} is (nx^{(1+n)/n})/(1+n)+C