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

The integral of ((\sqrt[3]{1+ln(x)})/x) is 3/4 (1+ln(x))^{4/3}+C

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integral of ((\sqrt[3]{1+ln(x)})/x)

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

\frac{3}{4} (1 + ln (x))^{\frac{4}{3}} + C

Solution steps

\int \frac{3 1 + 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 = 1 + ln (x)

= \frac{3}{4} (1 + ln (x))^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{4} (1 + ln (x))^{\frac{4}{3}} + C

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What is the integral of ((\sqrt[3]{1+ln(x)})/x) ?
The integral of ((\sqrt[3]{1+ln(x)})/x) is 3/4 (1+ln(x))^{4/3}+C