integral of x^3ln(9x^2)

Lösung

\int x^{3} ln (9 x^{2}) d x

\frac{1}{2} x^{4} ln (3 x) - \frac{x ^{4}}{8} + C

Schritte zur Lösung

\int x^{3} ln (9 x^{2}) d x

Wende die partielle Integration an

= \frac{1}{4} x^{4} ln (9 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 (9 x^{2}) - \frac{x ^{4}}{8}

\frac{1}{4} x^{4} ln (9 x^{2}) = \frac{1}{2} x^{4} ln (3 x)

= \frac{1}{2} x^{4} ln (3 x) - \frac{x ^{4}}{8}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{4} ln (3 x) - \frac{x ^{4}}{8} + C

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