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

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

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

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

diverges

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

diverges

= diverges

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