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

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

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

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

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

Solution steps

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

Simplify

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

(1 + x^{2} + y^{2} + x^{2} y^{2}) d y = (1 + y^{2}) d x

\int \frac{100}{100 - y} d y

y^{^{'''}} + 4 \cdot y^{^{'}} = 3 x - 1

x \to 1 lim (e^{4 x^{5} - 4 x})

\int (2 x - 1)^{2} d x

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