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

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

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

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

ln ∣ ln (ln (x)) ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ln ( u )} d u

= \int \frac{1}{u ln ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ ln (ln (x)) ∣

Add a constant to the solution

= ln ∣ ln (ln (x)) ∣ + C

f (x) = 1 1^{x}

\frac{\partial}{\partial x} (\frac{x + y + z}{3})

x \to 2 - lim (\frac{1}{x})

\frac{d}{d x} (\frac{2 - x}{x ^{2} + 4})

\int_{0}^{\frac{3}{2}} 9 - x^{2} d x

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