What is the integral from 8 to infinity of ln(x) ?

The integral from 8 to infinity of ln(x) is diverges

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integral from 8 to infinity of ln(x)

\int_{8}^{\infty} ln (x) d x

diverges

Solution steps

\int_{8}^{\infty} ln (x) d x

Compute the indefinite integral:

\int ln (x) d x = x ln (x) - x + C

Compute the boundaries:

\int_{8}^{\infty} ln (x) d x =

diverges

= diverges

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What is the integral from 8 to infinity of ln(x) ?
The integral from 8 to infinity of ln(x) is diverges