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Beliebt Rechnen >

integral of x(1-x^2)

Lösung

\int x (1 - x^{2}) d x

Lösung

\frac{x ^{2}}{2} - \frac{x ^{4}}{4} + C

Schritte zur Lösung

\int x (1 - x^{2}) d x

Multipliziere aus

x (1 - x^{2}) : x - x^{3}

= \int x - x^{3} 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 d x - \int x^{3} d x

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

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

= \frac{x ^{2}}{2} - \frac{x ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - \frac{x ^{4}}{4} + C

Graph

Beliebte Beispiele

integral of (x+sin(x))^2

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

laplacetransform tsin^2(t)

l a pl a ce t r an s f or m t sin^{2} (t)

integral of sec^2(θ)tan^4(θ)

\int sec^{2} (θ) tan^{4} (θ) d θ

2y^'=y^2,y(0)=7

2 y^{^{'}} = y^{2}, y (0) = 7

(d^2)/(dx^2)((x^2-2x)/(x+1))

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2} - 2 x}{x + 1})