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Beliebt Rechnen >

integral of 2ln(x)x^4

Lösung

\int 2 ln (x) x^{4} d x

Lösung

2 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

Schritte zur Lösung

\int 2 ln (x) x^{4} d x

Entferne die Konstante:

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

= 2 \cdot \int ln (x) x^{4} d x

Wende die partielle Integration an

= 2 (\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x)

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= 2 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

Füge eine Konstante zur Lösung hinzu

= 2 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

Graph

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