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

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

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integral of 1/(vln(v))

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

ln ∣ ln (v) ∣ + C

Solution steps

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

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 (v)

= ln ∣ ln (v) ∣

Add a constant to the solution

= ln ∣ ln (v) ∣ + C

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