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Beliebt Rechnen >

integral of (u+4)(2u+1)

Lösung

\int (u + 4) (2 u + 1) d u

Lösung

\frac{2 u ^{3}}{3} + \frac{9 u ^{2}}{2} + 4 u + C

Schritte zur Lösung

\int (u + 4) (2 u + 1) d u

Multipliziere aus

(u + 4) (2 u + 1) : 2 u^{2} + 9 u + 4

= \int 2 u^{2} + 9 u + 4 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 2 u^{2} d u + \int 9 u d u + \int 4 d u

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

\int 9 u d u = \frac{9 u ^{2}}{2}

\int 4 d u = 4 u

= \frac{2 u ^{3}}{3} + \frac{9 u ^{2}}{2} + 4 u

Füge eine Konstante zur Lösung hinzu

= \frac{2 u ^{3}}{3} + \frac{9 u ^{2}}{2} + 4 u + C

Graph

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