integral of x^6(2-x)

Lösung

\int x^{6} (2 - x) d x

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

Schritte zur Lösung

\int x^{6} (2 - x) d x

Multipliziere aus

x^{6} (2 - x) : 2 x^{6} - x^{7}

= \int 2 x^{6} - x^{7} 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^{6} d x - \int x^{7} d x

\int 2 x^{6} d x = \frac{2 x ^{7}}{7}

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

= \frac{2 x ^{7}}{7} - \frac{x ^{8}}{8}

Füge eine Konstante zur Lösung hinzu

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

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