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

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

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

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

diverges

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

diverges

= diverges

x \to \infty lim (- \frac{1}{2} e^{- x^{2}})

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