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

Lösung

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

- 2 ln^{2} (2) + 4 ln (2) + 5 ln^{2} (5) + 6 - 10 ln (5)

Dezimale

4.66875 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

- 2 ln^{2} (2) + 4 ln (2) + 5 ln^{2} (5) + 6 - 10 ln (5)

= - 2 ln^{2} (2) + 4 ln (2) + 5 ln^{2} (5) + 6 - 10 ln (5)

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