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

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

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

\int \frac{1}{x \cdot ( 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

x \to 1 lim (- x^{2} + 4 x - 8)

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\frac{\partial}{\partial x} (6 x cos (x) sin (y))

\frac{\partial}{\partial z} (4 ln (\frac{3 x y}{7 z}))

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