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

ln ∣ ln (x) ∣ + C

Solution steps

\int \frac{\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{e ^{- x}}{1 + e ^{- x}}

\frac{d}{d x} (2 (1 - sin (x)))

\int 8 x e^{4 x^{2}} d x

sin (x), \frac{π}{5}

f (x) = 4^{2}

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