integral of (2x^{10}+4x^9+x^8+10)

Lösung

\int (2 x^{10} + 4 x^{9} + x^{8} + 10) d x

\frac{2 x ^{11}}{11} + \frac{2 x ^{10}}{5} + \frac{x ^{9}}{9} + 10 x + C

Schritte zur Lösung

\int 2 x^{10} + 4 x^{9} + x^{8} + 10 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 2 x^{10} d x + \int 4 x^{9} d x + \int x^{8} d x + \int 10 d x

\int 2 x^{10} d x = \frac{2 x ^{11}}{11}

\int 4 x^{9} d x = \frac{2 x ^{10}}{5}

\int x^{8} d x = \frac{x ^{9}}{9}

\int 10 d x = 10 x

= \frac{2 x ^{11}}{11} + \frac{2 x ^{10}}{5} + \frac{x ^{9}}{9} + 10 x

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{11}}{11} + \frac{2 x ^{10}}{5} + \frac{x ^{9}}{9} + 10 x + C

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