What is the integral from 0 to e of (ln(x))^2 ?

The integral from 0 to e of (ln(x))^2 is e

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integral from 0 to e of (ln(x))^2

\int_{0}^{e} (ln (x))^{2} d x

e

Decimal

2.71828 \dots

Solution steps

\int_{0}^{e} (ln (x))^{2} d x

Apply Integration By Parts

: [x ln^{2} (x) - \int 2 ln (x) d x]_{0}^{e}

= [x ln^{2} (x) - \int 2 ln (x) d x]_{0}^{e}

\int 2 ln (x) d x = 2 (x ln (x) - x)

= [x ln^{2} (x) - 2 (x ln (x) - x)]_{0}^{e}

Compute the boundaries:

e

= e

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What is the integral from 0 to e of (ln(x))^2 ?
The integral from 0 to e of (ln(x))^2 is e