What is the integral of 8ln(\sqrt[3]{x}) ?

The integral of 8ln(\sqrt[3]{x}) is 8(1/3 xln(x)-1/3 x)+C

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integral of 8ln(\sqrt[3]{x})

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

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply Integration By Parts

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

Simplify

= 8 (\frac{1}{3} x ln (x) - \frac{1}{3} x)

Add a constant to the solution

= 8 (\frac{1}{3} x ln (x) - \frac{1}{3} x) + C

What is the integral of 8ln(\sqrt[3]{x}) ?
The integral of 8ln(\sqrt[3]{x}) is 8(1/3 xln(x)-1/3 x)+C