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Beliebt Rechnen >

integral of 8xln(7x)

Lösung

\int 8 x ln (7 x) d x

Lösung

8 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}) + C

Schritte zur Lösung

\int 8 x ln (7 x) d x

Entferne die Konstante:

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

= 8 \cdot \int x ln (7 x) d x

Wende die partielle Integration an

= 8 (\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x)

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 8 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4})

Füge eine Konstante zur Lösung hinzu

= 8 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}) + C

Graph

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