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

Lösung

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

e

Dezimale

2.71828 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [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}

Berechne die Grenzen:

e

= e

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