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

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

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

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

\frac{2}{e}

Decimal Notation

0.73575 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

\frac{2}{e}

= \frac{2}{e}

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