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})

\int 8 ln (3 x) d x

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

Solution steps

\int 8 ln (3 x) d x

Take the constant out:

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

= 8 \cdot \int ln (3 x) d x

Apply Integration By Parts

: x ln (3 x) - \int \frac{1}{3} d x

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

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

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

Simplify

ln (3 x) : \frac{1}{3} ln (x)

= 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

\int_{1}^{2} ln (3 x) d x

\int \frac{sin ( 2 x )}{33 + cos ^{2} ( x )} d x

\frac{d}{d x} ((x^{2} + 3) \cdot x)

x^{2} + 36

x \to 1 + lim (x^{\frac{1}{( x - 1 )}})

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