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Beliebt Rechnen >

integral of 6xln(x^6)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

\int 3 x d x = \frac{3 x ^{2}}{2}

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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