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Beliebt Rechnen >

integral of (ln(x^3))^2

Lösung

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

Lösung

9 x ln^{2} (x) - 6 (3 x ln (x) - 3 x) + C

Schritte zur Lösung

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

Vereinfache

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

Wende die partielle Integration an

= x ln^{2} (x^{3}) - \int 6 ln (x^{3}) d x

\int 6 ln (x^{3}) d x = 6 (3 x ln (x) - 3 x)

= x ln^{2} (x^{3}) - 6 (3 x ln (x) - 3 x)

Vereinfache

x ln^{2} (x^{3}) - 6 (3 x ln (x) - 3 x) : 9 x ln^{2} (x) - 6 (3 x ln (x) - 3 x)

= 9 x ln^{2} (x) - 6 (3 x ln (x) - 3 x)

Füge eine Konstante zur Lösung hinzu

= 9 x ln^{2} (x) - 6 (3 x ln (x) - 3 x) + C

Graph

Beliebte Beispiele

5 y^{^{'}} + 45 y = 9

integral of 1/(12x^3)

\int \frac{1}{12 x ^{3}} d x

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\int_{0}^{1} e^{x} - 1 d x

integral of sin(ln(6x))

\int sin (ln (6 x)) d x