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

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

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

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

ln ∣ 1 + ln (x) ∣ + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + ln (x)

= ln ∣ 1 + ln (x) ∣

Add a constant to the solution

= ln ∣ 1 + ln (x) ∣ + C

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