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

The integral of ln(\sqrt[3]{x}) is 1/3 xln(x)-1/3 x+C

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

\frac{1}{3} x ln (x) - \frac{1}{3} x + C

Solution steps

Apply Integration By Parts

\int \frac{1}{3} d x = \frac{1}{3} x

Simplify

= \frac{1}{3} x ln (x) - \frac{1}{3} x

Add a constant to the solution

= \frac{1}{3} x ln (x) - \frac{1}{3} x + C

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What is the integral of ln(\sqrt[3]{x}) ?
The integral of ln(\sqrt[3]{x}) is 1/3 xln(x)-1/3 x+C