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Beliebt Rechnen >

integral of (-ln(x))^2

Lösung

\int (- ln (x))^{2} d x

Lösung

x ln^{2} (x) - 2 (x ln (x) - x) + C

Schritte zur Lösung

\int (- ln (x))^{2} d x

Vereinfache

(- ln (x))^{2} : ln^{2} (x)

= \int ln^{2} (x) d x

Wende die partielle Integration an

= x ln^{2} (x) - \int 2 ln (x) d x

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

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

Füge eine Konstante zur Lösung hinzu

= x ln^{2} (x) - 2 (x ln (x) - x) + C

Graph

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