integral from 0 to 5 of (ln(x))^2

Lösung

\int_{0}^{5} (ln (x))^{2} d x

5 ln^{2} (5) - 2 (5 ln (5) - 5)

Dezimale

6.85707 \dots

Schritte zur Lösung

\int_{0}^{5} (ln (x))^{2} d x

Wende die partielle Integration an

= [x ln^{2} (x) - \int 2 ln (x) d x]_{0}^{5}

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

= [x ln^{2} (x) - 2 (x ln (x) - x)]_{0}^{5}

Berechne die Grenzen:

5 ln^{2} (5) - 2 (5 ln (5) - 5)

= 5 ln^{2} (5) - 2 (5 ln (5) - 5)

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