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Beliebt Rechnen >

integral (ln(x))^3

Lösung

integral

(ln (x))^{3}

Lösung

x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

Schritte zur Lösung

\int (ln (x))^{3} d x

Wende die partielle Integration an

= x ln^{3} (x) - \int 3 ln^{2} (x) d x

\int 3 ln^{2} (x) d x = 3 (x ln^{2} (x) - 2 (x ln (x) - x))

= x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))

Füge eine Konstante zur Lösung hinzu

= x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

Graph

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