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Beliebt Rechnen >

integral of x^9(5+x^{10})

Lösung

\int x^{9} (5 + x^{10}) d x

Lösung

\frac{x ^{10}}{2} + \frac{x ^{20}}{20} + C

Schritte zur Lösung

\int x^{9} (5 + x^{10}) d x

Multipliziere aus

x^{9} (5 + x^{10}) : 5 x^{9} + x^{19}

= \int 5 x^{9} + x^{19} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 x^{9} d x + \int x^{19} d x

\int 5 x^{9} d x = \frac{x ^{10}}{2}

\int x^{19} d x = \frac{x ^{20}}{20}

= \frac{x ^{10}}{2} + \frac{x ^{20}}{20}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{10}}{2} + \frac{x ^{20}}{20} + C

Graph

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