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Beliebt Rechnen >

integral of x(x^2-4)

Lösung

\int x (x^{2} - 4) d x

Lösung

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

Schritte zur Lösung

\int x (x^{2} - 4) d x

Multipliziere aus

x (x^{2} - 4) : x^{3} - 4 x

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

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

\int 4 x d x = 2 x^{2}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

sum from n=1 to infinity of 2/(nln(7n))

n = 1 \sum \infty \frac{2}{n ln ( 7 n )}

integral of sin(x/3)

\int sin (\frac{x}{3}) d x

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\int 7 x^{6} d x

(\partial)/(\partial y)(3x-2y^4)

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integral of (x^2)/(x^3-2)

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