integral of [u^5-u^3+u^2]

Lösung

\int [u^{5} - u^{3} + u^{2}] d u

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

Schritte zur Lösung

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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