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Beliebt Rechnen >

integral of z(ln(z))^2

Lösung

\int z (ln (z))^{2} d z

Lösung

\frac{1}{2} z^{2} ln^{2} (z) - \frac{1}{2} z^{2} ln (z) + \frac{z ^{2}}{4} + C

Schritte zur Lösung

\int z (ln (z))^{2} d z

Wende die partielle Integration an

= \frac{1}{2} z^{2} ln^{2} (z) - \int z ln (z) d z

\int z ln (z) d z = \frac{1}{2} z^{2} ln (z) - \frac{z ^{2}}{4}

= \frac{1}{2} z^{2} ln^{2} (z) - (\frac{1}{2} z^{2} ln (z) - \frac{z ^{2}}{4})

Vereinfache

= \frac{1}{2} z^{2} ln^{2} (z) - \frac{1}{2} z^{2} ln (z) + \frac{z ^{2}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} z^{2} ln^{2} (z) - \frac{1}{2} z^{2} ln (z) + \frac{z ^{2}}{4} + C

Graph

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