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Beliebt Rechnen >

integral of (x+3)^2

Lösung

\int (x + 3)^{2} d x

Lösung

\frac{x ^{3}}{3} + 3 x^{2} + 9 x + C

Schritte zur Lösung

\int (x + 3)^{2} d x

Multipliziere aus

(x + 3)^{2} : x^{2} + 6 x + 9

= \int x^{2} + 6 x + 9 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 x^{2} d x + \int 6 x d x + \int 9 d x

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

\int 6 x d x = 3 x^{2}

\int 9 d x = 9 x

= \frac{x ^{3}}{3} + 3 x^{2} + 9 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + 3 x^{2} + 9 x + C

Graph

Beliebte Beispiele

integral from 0 to x of 3e^{-3x}

\int_{0}^{x} 3 e^{- 3 x} d x

limit as x approaches infinity of 13x

x \to \infty lim (13 x)

integral of x^9sqrt(x^5+7)

\int x^{9} x^{5} + 7 d x

derivative (x^2-25)/(x-5)

d er i v a t i v e \frac{x ^{2} - 25}{x - 5}

y^{^{'}} = \frac{y ^{2}}{x}