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

The integral of (\sqrt[3]{ln(x)})/x is 3/4 ln^{4/3}(x)+C

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

\int \frac{3 ln ( x )}{x} d x

\frac{3}{4} ln^{\frac{4}{3}} (x) + C

Solution steps

\int \frac{3 ln ( x )}{x} d x

Apply u-substitution

: \int 3 u d u

= \int 3 u d u

Apply the Power Rule

: \frac{3}{4} u^{\frac{4}{3}}

= \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = ln (x)

= \frac{3}{4} ln^{\frac{4}{3}} (x)

Add a constant to the solution

= \frac{3}{4} ln^{\frac{4}{3}} (x) + C

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What is the integral of (\sqrt[3]{ln(x)})/x ?
The integral of (\sqrt[3]{ln(x)})/x is 3/4 ln^{4/3}(x)+C