What is the integral of 1/(vln(v)-v) ?

The integral of 1/(vln(v)-v) is ln|ln(v)-1|+C

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integral of 1/(vln(v)-v)

\int \frac{1}{v ln ( v ) - v} d v

ln ∣ ln (v) - 1 ∣ + C

Solution steps

\int \frac{1}{v ln ( v ) - v} d v

Apply u-substitution

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

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{w} d w = ln (∣ w ∣)

= ln ∣ w ∣

Substitute back

= ln ∣ ln (v) - 1 ∣

Add a constant to the solution

= ln ∣ ln (v) - 1 ∣ + C

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What is the integral of 1/(vln(v)-v) ?
The integral of 1/(vln(v)-v) is ln|ln(v)-1|+C