integral from 3 to 4 of (ln(x))^2

Lösung

\int_{3}^{4} (ln (x))^{2} d x

16 ln^{2} (2) - 16 ln (2) + 2 + 6 ln (3) - 3 ln^{2} (3)

Dezimale

1.56772 \dots

Schritte zur Lösung

\int_{3}^{4} (ln (x))^{2} d x

Wende die partielle Integration an

= [x ln^{2} (x) - \int 2 ln (x) d x]_{3}^{4}

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

= [x ln^{2} (x) - 2 (x ln (x) - x)]_{3}^{4}

Berechne die Grenzen:

16 ln^{2} (2) - 16 ln (2) + 2 + 6 ln (3) - 3 ln^{2} (3)

= 16 ln^{2} (2) - 16 ln (2) + 2 + 6 ln (3) - 3 ln^{2} (3)

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