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 ( 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^{2} - 3 x - 5

\int_{- 14}^{7} 7 e^{x} d x

\frac{d}{d x} (\frac{x ^{3} - 3 x ^{2}}{( x - 1 ) ^{3}})

y = \frac{8 x}{8 + x}

y^{^{''}} - y^{^{'}} = 5 sin (2 x)

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