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Beliebt Rechnen >

integral of (x^2+3)^2

Lösung

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

Lösung

\frac{x ^{5}}{5} + 2 x^{3} + 9 x + C

Schritte zur Lösung

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

Multipliziere aus

(x^{2} + 3)^{2} : x^{4} + 6 x^{2} + 9

= \int x^{4} + 6 x^{2} + 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^{4} d x + \int 6 x^{2} d x + \int 9 d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 9 d x = 9 x

= \frac{x ^{5}}{5} + 2 x^{3} + 9 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} + 2 x^{3} + 9 x + C

Graph

Beliebte Beispiele

derivative 6x^{2/3}

d er i v a t i v e 6 x^{\frac{2}{3}}

integral of e^{-5r}

\int e^{- 5 r} d r

derivative y=e^{2x-x^2}

d er i v a t i v e y = e^{2 x - x^{2}}

(dy)/(dx)=(8x)/(7y)

\frac{d y}{d x} = \frac{8 x}{7 y}

integral of ln((1+x)/(1-x))

\int ln (\frac{1 + x}{1 - x}) d x