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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{4} x^{4} (ln (2) + 2 ln (x)) - \frac{x ^{4}}{8} + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{4} x^{4} ln (2 x^{2}) - \int \frac{x ^{3}}{2} d x

\int \frac{x ^{3}}{2} d x = \frac{x ^{4}}{8}

= \frac{1}{4} x^{4} ln (2 x^{2}) - \frac{x ^{4}}{8}

Vereinfache

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

= \frac{1}{4} x^{4} (ln (2) + 2 ln (x)) - \frac{x ^{4}}{8}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x^{4} (ln (2) + 2 ln (x)) - \frac{x ^{4}}{8} + C

Graph

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