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

The integral of 1/(x\sqrt[3]{ln(x))} is 3/2 ln^{2/3}(x)+C

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

\frac{3}{2} ln^{\frac{2}{3}} (x) + C

Solution steps

Apply u-substitution

Apply the Power Rule

: \frac{3}{2} u^{\frac{2}{3}}

= \frac{3}{2} u^{\frac{2}{3}}

Substitute back

u = ln (x)

= \frac{3}{2} ln^{\frac{2}{3}} (x)

Add a constant to the solution

= \frac{3}{2} ln^{\frac{2}{3}} (x) + C

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What is the integral of 1/(x\sqrt[3]{ln(x))} ?
The integral of 1/(x\sqrt[3]{ln(x))} is 3/2 ln^{2/3}(x)+C