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Beliebt Rechnen >

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

Lösung

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

Lösung

x + \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - \frac{x ^{4}}{2} + C

Schritte zur Lösung

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

Multipliziere aus

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

= \int 1 + 2 x^{2} - x - 2 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 1 d x + \int 2 x^{2} d x - \int x d x - \int 2 x^{3} d x

\int 1 d x = x

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

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

= x + \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - \frac{x ^{4}}{2}

Füge eine Konstante zur Lösung hinzu

= x + \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - \frac{x ^{4}}{2} + C

Graph

Beliebte Beispiele

integral of (x^2)/(x^6-1)

\int \frac{x ^{2}}{x ^{6} - 1} d x

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

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

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

integral of x^2(x^2-49)^{3/2}

\int x^{2} (x^{2} - 49)^{\frac{3}{2}} d x