integral of x^9ln(7x^5)

Lösung

\int x^{9} ln (7 x^{5}) d x

\frac{1}{10} x^{10} (ln (7) + 5 ln (x)) - \frac{x ^{10}}{20} + C

Schritte zur Lösung

\int x^{9} ln (7 x^{5}) d x

Wende die partielle Integration an

= \frac{1}{10} x^{10} ln (7 x^{5}) - \int \frac{x ^{9}}{2} d x

\int \frac{x ^{9}}{2} d x = \frac{x ^{10}}{20}

= \frac{1}{10} x^{10} ln (7 x^{5}) - \frac{x ^{10}}{20}

Vereinfache

ln (7 x^{5}) : 5 ln (x) + ln (7)

= \frac{1}{10} x^{10} (ln (7) + 5 ln (x)) - \frac{x ^{10}}{20}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{10} x^{10} (ln (7) + 5 ln (x)) - \frac{x ^{10}}{20} + C

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