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

= \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

t^{2} y^{^{''}} + t y^{^{'}} + y = 0

\frac{d}{d x} (e^{4 x} + 4 e^{4 x} x)

\int \frac{2 x ^{3} + 3 x}{x ^{4} + 3 x ^{2} + 7} d x

\int \frac{31}{x ^{3} - 125} d x

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