What is the integral from 1 to e of ln|x| ?

The integral from 1 to e of ln|x| is 1

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integral from 1 to e of ln|x|

\int_{1}^{e} ln ∣ x ∣ d x

1

Solution steps

\int_{1}^{e} ln ∣ x ∣ d x

Eliminate Absolutes

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

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{1}^{e}

= [x ln (x) - \int 1 d x]_{1}^{e}

\int 1 d x = x

= [x ln (x) - x]_{1}^{e}

Compute the boundaries:

1

= 1

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What is the integral from 1 to e of ln|x| ?
The integral from 1 to e of ln|x| is 1