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Beliebt Rechnen >

integral of x^{15}ln(9x^8)

Lösung

\int x^{15} ln (9 x^{8}) d x

Lösung

\frac{1}{8} x^{16} (ln (3) + 4 ln (x)) - \frac{x ^{16}}{32} + C

Schritte zur Lösung

\int x^{15} ln (9 x^{8}) d x

Wende die partielle Integration an

= \frac{1}{16} x^{16} ln (9 x^{8}) - \int \frac{x ^{15}}{2} d x

\int \frac{x ^{15}}{2} d x = \frac{x ^{16}}{32}

= \frac{1}{16} x^{16} ln (9 x^{8}) - \frac{x ^{16}}{32}

\frac{1}{16} x^{16} ln (9 x^{8}) = \frac{1}{8} x^{16} (ln (3) + 4 ln (x))

= \frac{1}{8} x^{16} (ln (3) + 4 ln (x)) - \frac{x ^{16}}{32}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{8} x^{16} (ln (3) + 4 ln (x)) - \frac{x ^{16}}{32} + C

Graph

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