integral of x^5(ln(x))^2

Lösung

\int x^{5} (ln (x))^{2} d x

\frac{1}{6} x^{6} ln^{2} (x) - \frac{1}{3} (\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}) + C

Schritte zur Lösung

\int x^{5} (ln (x))^{2} d x

Wende die partielle Integration an

= \frac{1}{6} x^{6} ln^{2} (x) - \int \frac{1}{3} x^{5} ln (x) d x

\int \frac{1}{3} x^{5} ln (x) d x = \frac{1}{3} (\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36})

= \frac{1}{6} x^{6} ln^{2} (x) - \frac{1}{3} (\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{6} x^{6} ln^{2} (x) - \frac{1}{3} (\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}) + C

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