integral of (u^6-2u^5-u^3+2/7)

Lösung

\int (u^{6} - 2 u^{5} - u^{3} + \frac{2}{7}) d u

\frac{u ^{7}}{7} - \frac{u ^{6}}{3} - \frac{u ^{4}}{4} + \frac{2}{7} u + C

Schritte zur Lösung

\int u^{6} - 2 u^{5} - u^{3} + \frac{2}{7} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{6} d u - \int 2 u^{5} d u - \int u^{3} d u + \int \frac{2}{7} d u

\int u^{6} d u = \frac{u ^{7}}{7}

\int 2 u^{5} d u = \frac{u ^{6}}{3}

\int u^{3} d u = \frac{u ^{4}}{4}

\int \frac{2}{7} d u = \frac{2}{7} u

= \frac{u ^{7}}{7} - \frac{u ^{6}}{3} - \frac{u ^{4}}{4} + \frac{2}{7} u

Füge eine Konstante zur Lösung hinzu

= \frac{u ^{7}}{7} - \frac{u ^{6}}{3} - \frac{u ^{4}}{4} + \frac{2}{7} u + C

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