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

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

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

ln ∣ ln (x) ∣ + C

Solution steps

assuming

ln (x) \geq 0

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

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = ln (x)

= ln ∣ ln (x) ∣

Add a constant to the solution

= ln ∣ ln (x) ∣ + C

\frac{d x}{d t} = 4000 - \frac{x}{50 + t}

\frac{x ^{2} + 1}{x ^{2} + 1 + x}

n = 1 \sum \infty \frac{( - 1 ) ^{n}}{n ( n ^{2} + 1 ) ^{\frac{1}{2}}}

\frac{\partial}{\partial x} (- x y z^{2} + 27)

\frac{d}{d x} (ln (x^{2} - 9 x + 1))

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