integral of 6x^5ln(x)

Lösung

\int 6 x^{5} ln (x) d x

x^{6} ln (x) - \frac{x ^{6}}{6} + C

Schritte zur Lösung

\int 6 x^{5} ln (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int x^{5} ln (x) d x

Wende die partielle Integration an

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

\int \frac{x ^{5}}{6} d x = \frac{x ^{6}}{36}

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

Vereinfache

6 (\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}) : x^{6} ln (x) - \frac{x ^{6}}{6}

= x^{6} ln (x) - \frac{x ^{6}}{6}

Füge eine Konstante zur Lösung hinzu

= x^{6} ln (x) - \frac{x ^{6}}{6} + C

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