What is the integral of 1/(\sqrt[n]{x)} ?

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

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