What is the integral of 1/(xln(x)-2x) ?

The integral of 1/(xln(x)-2x) is ln|ln(x)-2|+C

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integral of 1/(xln(x)-2x)

\int \frac{1}{x ln ( x ) - 2 x} d x

ln ∣ ln (x) - 2 ∣ + C

Solution steps

\int \frac{1}{x ln ( x ) - 2 x} d x

Apply u-substitution

= \int \frac{1}{u - 2} d u

Apply u-substitution

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ ln (x) - 2 ∣

Add a constant to the solution

= ln ∣ ln (x) - 2 ∣ + C

What is the integral of 1/(xln(x)-2x) ?
The integral of 1/(xln(x)-2x) is ln|ln(x)-2|+C