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Beliebt Rechnen >

integral of (1+u+u^2)

Lösung

\int (1 + u + u^{2}) d u

Lösung

u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3} + C

Schritte zur Lösung

\int 1 + u + 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 1 d u + \int u d u + \int u^{2} d u

\int 1 d u = u

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

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

= u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3} + C

Graph

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