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

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

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

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

- \frac{2}{ln ( x )} + C

Solution steps

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

Apply u-substitution

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

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

Simplify

u u : u^{\frac{3}{2}}

= \int \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

: - \frac{2}{u}

= - \frac{2}{u}

Substitute back

u = ln (x)

= - \frac{2}{ln ( x )}

Add a constant to the solution

= - \frac{2}{ln ( x )} + C

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