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

\frac{d}{d x} (4 x + 10)

x \to 1 lim (3^{\frac{1}{x}})

\int \frac{4 x}{4 x ^{2} + 5} d x

\frac{d}{d x} (a x cos (x) + b cos (x))

\frac{d}{d x} (e^{- (x^{2} + y^{2} + z^{2})})

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