What is the integral from 0 to infinity of (ln(x))/x ?

The integral from 0 to infinity of (ln(x))/x is diverges

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integral from 0 to infinity of (ln(x))/x

\int_{0}^{\infty} \frac{ln ( x )}{x} d x

diverges

Solution steps

\int_{0}^{\infty} \frac{ln ( x )}{x} d x

Compute the indefinite integral:

\int \frac{ln ( x )}{x} d x = \frac{ln ^{2} ( x )}{2} + C

Compute the boundaries:

\int_{0}^{\infty} \frac{ln ( x )}{x} d x =

diverges

= diverges

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x \to 0 - lim (4)

What is the integral from 0 to infinity of (ln(x))/x ?
The integral from 0 to infinity of (ln(x))/x is diverges