integral from 1 to 2 of (ln(4x))^2

Lösung

\int_{1}^{2} (ln (4 x))^{2} d x

14 ln^{2} (2) - 8 ln (2) + 2

Dezimale

3.18116 \dots

Schritte zur Lösung

\int_{1}^{2} (ln (4 x))^{2} d x

Wende die partielle Integration an

= [x ln^{2} (4 x) - \int 2 ln (4 x) d x]_{1}^{2}

\int 2 ln (4 x) d x = 2 (x ln (4 x) - x)

= [x ln^{2} (4 x) - 2 (x ln (4 x) - x)]_{1}^{2}

Berechne die Grenzen:

14 ln^{2} (2) - 8 ln (2) + 2

= 14 ln^{2} (2) - 8 ln (2) + 2

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