integral of x^7ln(9x^4)

Lösung

\int x^{7} ln (9 x^{4}) d x

\frac{1}{4} x^{8} (ln (3) + 2 ln (x)) - \frac{x ^{8}}{16} + C

Schritte zur Lösung

\int x^{7} ln (9 x^{4}) d x

Wende die partielle Integration an

= \frac{1}{8} x^{8} ln (9 x^{4}) - \int \frac{x ^{7}}{2} d x

\int \frac{x ^{7}}{2} d x = \frac{x ^{8}}{16}

= \frac{1}{8} x^{8} ln (9 x^{4}) - \frac{x ^{8}}{16}

\frac{1}{8} x^{8} ln (9 x^{4}) = \frac{1}{4} x^{8} (ln (3) + 2 ln (x))

= \frac{1}{4} x^{8} (ln (3) + 2 ln (x)) - \frac{x ^{8}}{16}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x^{8} (ln (3) + 2 ln (x)) - \frac{x ^{8}}{16} + C

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