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

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

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

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

ln ∣ ln (x) ∣ + C

Solution steps

\int \frac{1}{x 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 = ln (x)

= ln ∣ ln (x) ∣

Add a constant to the solution

= ln ∣ ln (x) ∣ + C

\int \frac{8 + 3 x}{x ( x ^{2} + 4 )} d x

x^{3} - 15 x^{2} + 72 x

\int \frac{1}{3 1 + 2 x} d x

\int \frac{1}{12 x - x ^{2}} d x

\frac{d}{d x} (\frac{ln ( 5 x )}{5 x})

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