integral of x^3ln(8x)

Lösung

\int x^{3} ln (8 x) d x

\frac{1}{4} x^{4} ln (8 x) - \frac{x ^{4}}{16} + C

Schritte zur Lösung

\int x^{3} ln (8 x) d x

Wende die partielle Integration an

= \frac{1}{4} x^{4} ln (8 x) - \int \frac{x ^{3}}{4} d x

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= \frac{1}{4} x^{4} ln (8 x) - \frac{x ^{4}}{16}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x^{4} ln (8 x) - \frac{x ^{4}}{16} + C

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