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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{3} ln (2) x^{3} + x^{3} ln (x) - \frac{x ^{3}}{3} + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{3} x^{3} ln (2 x^{3}) - \int x^{2} d x

\int x^{2} d x = \frac{x ^{3}}{3}

= \frac{1}{3} x^{3} ln (2 x^{3}) - \frac{x ^{3}}{3}

Vereinfache

\frac{1}{3} x^{3} ln (2 x^{3}) - \frac{x ^{3}}{3} : \frac{1}{3} ln (2) x^{3} + x^{3} ln (x) - \frac{x ^{3}}{3}

= \frac{1}{3} ln (2) x^{3} + x^{3} ln (x) - \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} ln (2) x^{3} + x^{3} ln (x) - \frac{x ^{3}}{3} + C

Graph

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