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Beliebt Rechnen >

integral of (1-x^2)x

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

(1 - x^{2}) x : 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 (3x^2+2x-7)/(x^2-3x+2)

\int \frac{3 x ^{2} + 2 x - 7}{x ^{2} - 3 x + 2} d x

integral of (\sqrt[3]{x})/(sqrt(x)-1)

\int \frac{3 x}{x - 1} d x

integral of pir^2

\int π r^{2} d r

integral of 1/(x^2+2x-1)

\int \frac{1}{x ^{2} + 2 x - 1} d x

integral of x^3(1+x^4)^4

\int x^{3} (1 + x^{4})^{4} d x