What is the integral of 1/(x\sqrt[3]{ln(x^5))} ?

The integral of 1/(x\sqrt[3]{ln(x^5))} is 3/(2\sqrt[3]{5)}ln^{2/3}(x)+C

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integral of 1/(x\sqrt[3]{ln(x^5))}

Solution steps

Take the constant out:

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

Apply u-substitution

Apply the Power Rule

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

Substitute back

u = ln (x)

Simplify

Add a constant to the solution

\int x^{5} arctan (x^{2}) d x

\int 2 x^{3} sin (x^{4}) d x

\int \frac{y ^{2}}{( y ^{2} + 16 ) ^{\frac{3}{2}}} d y

\int \frac{1}{csc ^{2} ( u ) sec ^{5} ( u )} d u

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

What is the integral of 1/(x\sqrt[3]{ln(x^5))} ?
The integral of 1/(x\sqrt[3]{ln(x^5))} is 3/(2\sqrt[3]{5)}ln^{2/3}(x)+C