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

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

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integral from 1 to e of ln^2(x)

\int_{1}^{e} ln^{2} (x) d x

e - 2

Decimal

0.71828 \dots

Solution steps

\int_{1}^{e} ln^{2} (x) d x

Apply Integration By Parts

= [x ln^{2} (x) - \int 2 ln (x) d x]_{1}^{e}

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

= [x ln^{2} (x) - 2 (x ln (x) - x)]_{1}^{e}

Compute the boundaries:

e - 2

= e - 2

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