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

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

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

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

ln ∣ ln (x) - 1 ∣ + C

Solution steps

\int \frac{1}{x ( ln ( x ) - 1 )} 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) - 1

= ln ∣ ln (x) - 1 ∣

Add a constant to the solution

= ln ∣ ln (x) - 1 ∣ + C

\int \frac{lo g _{3} ( x )}{3 x} d x

\int sin (4 x) cos^{2} (2 x) sin (x) d x

tan (3) x^{2}

\frac{\partial}{\partial x} (y^{x^{2} - y})

3 t - 4 t^{2}

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