integral of 3x^{10}-x^5+2x-9

Lösung

\int 3 x^{10} - x^{5} + 2 x - 9 d x

\frac{3 x ^{11}}{11} - \frac{x ^{6}}{6} + x^{2} - 9 x + C

Schritte zur Lösung

\int 3 x^{10} - x^{5} + 2 x - 9 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 3 x^{10} d x - \int x^{5} d x + \int 2 x d x - \int 9 d x

\int 3 x^{10} d x = \frac{3 x ^{11}}{11}

\int x^{5} d x = \frac{x ^{6}}{6}

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

\int 9 d x = 9 x

= \frac{3 x ^{11}}{11} - \frac{x ^{6}}{6} + x^{2} - 9 x

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{11}}{11} - \frac{x ^{6}}{6} + x^{2} - 9 x + C

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