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

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

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integral from 2 to infinity of 1/(x(ln(x)))

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

diverges

Solution steps

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

Compute the indefinite integral:

\int \frac{1}{x ln ( x )} d x = ln ∣ ln (x) ∣ + C

Compute the boundaries:

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

diverges

= diverges

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