What is the integral from 1/2 to 1 of 1/(xln(x)) ?

The integral from 1/2 to 1 of 1/(xln(x)) is diverges

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integral from 1/2 to 1 of 1/(xln(x))

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

diverges

Solution steps

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

Apply u-substitution

: \int_{- l n (2)}^{0} \frac{1}{u} d u

= \int_{- l n (2)}^{0} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- l n (2)}^{0}

Compute the boundaries:

diverges

= diverges

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What is the integral from 1/2 to 1 of 1/(xln(x)) ?
The integral from 1/2 to 1 of 1/(xln(x)) is diverges