What is the integral of 1/(x*ln(x)*ln(ln(x))) ?

The integral of 1/(x*ln(x)*ln(ln(x))) is ln|ln(ln(x))|+C

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integral of 1/(xln(x)ln(ln(x)))

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

ln ∣ ln (ln (x)) ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ln ( u )} d u

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ ln (ln (x)) ∣

Add a constant to the solution

= ln ∣ ln (ln (x)) ∣ + C

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What is the integral of 1/(x*ln(x)*ln(ln(x))) ?
The integral of 1/(x*ln(x)*ln(ln(x))) is ln|ln(ln(x))|+C