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Beliebt Rechnen >

integral of (x-1)^9

Lösung

\int (x - 1)^{9} d x

Lösung

x (x - 1)^{9} - \frac{9}{10} (x - 1)^{10} - (x - 1)^{9} + C

Schritte zur Lösung

\int (x - 1)^{9} d x

Wende die partielle Integration an

= (x - 1)^{9} x - \int 9 (x - 1)^{8} x d x

\int 9 (x - 1)^{8} x d x = \frac{9}{10} (x - 1)^{10} + (x - 1)^{9}

= (x - 1)^{9} x - (\frac{9}{10} (x - 1)^{10} + (x - 1)^{9})

Vereinfache

(x - 1)^{9} x - (\frac{9}{10} (x - 1)^{10} + (x - 1)^{9}) : x (x - 1)^{9} - \frac{9}{10} (x - 1)^{10} - (x - 1)^{9}

= x (x - 1)^{9} - \frac{9}{10} (x - 1)^{10} - (x - 1)^{9}

Füge eine Konstante zur Lösung hinzu

= x (x - 1)^{9} - \frac{9}{10} (x - 1)^{10} - (x - 1)^{9} + C

Graph

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