What is the integral of 1/(xln(x)ln^2(ln(x))) ?

The integral of 1/(xln(x)ln^2(ln(x))) is -1/(ln(ln(x)))+C

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integral of 1/(xln(x)ln^2(ln(x)))

\int \frac{1}{x ln ( x ) ln ^{2} ( ln ( x ) )} d x

- \frac{1}{ln ( ln ( x ) )} + C

Solution steps

\int \frac{1}{x ln ( x ) ln ^{2} ( ln ( x ) )} d x

Apply u-substitution

: \int \frac{1}{u ln ^{2} ( u )} d u

= \int \frac{1}{u ln ^{2} ( u )} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= - \frac{1}{v}

Substitute back

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

Add a constant to the solution

= - \frac{1}{ln ( ln ( x ) )} + C

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What is the integral of 1/(xln(x)ln^2(ln(x))) ?
The integral of 1/(xln(x)ln^2(ln(x))) is -1/(ln(ln(x)))+C