integral of (x^3-2x^2)^3

Lösung

\int (x^{3} - 2 x^{2})^{3} d x

\frac{x ^{10}}{10} - \frac{2 x ^{9}}{3} + \frac{3 x ^{8}}{2} - \frac{8 x ^{7}}{7} + C

Schritte zur Lösung

\int (x^{3} - 2 x^{2})^{3} d x

Multipliziere aus

(x^{3} - 2 x^{2})^{3} : x^{9} - 6 x^{8} + 12 x^{7} - 8 x^{6}

= \int x^{9} - 6 x^{8} + 12 x^{7} - 8 x^{6} 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 x^{9} d x - \int 6 x^{8} d x + \int 12 x^{7} d x - \int 8 x^{6} d x

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

\int 6 x^{8} d x = \frac{2 x ^{9}}{3}

\int 12 x^{7} d x = \frac{3 x ^{8}}{2}

\int 8 x^{6} d x = \frac{8 x ^{7}}{7}

= \frac{x ^{10}}{10} - \frac{2 x ^{9}}{3} + \frac{3 x ^{8}}{2} - \frac{8 x ^{7}}{7}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{10}}{10} - \frac{2 x ^{9}}{3} + \frac{3 x ^{8}}{2} - \frac{8 x ^{7}}{7} + C