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

\int \frac{1}{x ^{2} - 4 x + 5} d x

x^{2} y^{^{'}} + 2 x y = 15 cos^{2} (x)

\int_{- 1}^{2} x^{2} - 2 x d x

f (x) = 4 - x

x \to 0 + lim (x^{3 s i n (x)})

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