integral of (9x^8+10x^5-5x^2-5)

Lösung

\int (9 x^{8} + 10 x^{5} - 5 x^{2} - 5) d x

x^{9} + \frac{5 x ^{6}}{3} - \frac{5 x ^{3}}{3} - 5 x + C

Schritte zur Lösung

\int 9 x^{8} + 10 x^{5} - 5 x^{2} - 5 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 9 x^{8} d x + \int 10 x^{5} d x - \int 5 x^{2} d x - \int 5 d x

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

\int 10 x^{5} d x = \frac{5 x ^{6}}{3}

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 5 d x = 5 x

= x^{9} + \frac{5 x ^{6}}{3} - \frac{5 x ^{3}}{3} - 5 x

Füge eine Konstante zur Lösung hinzu

= x^{9} + \frac{5 x ^{6}}{3} - \frac{5 x ^{3}}{3} - 5 x + C

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