de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (6x^2+4x-3)

\int (6 x^{2} + 4 x - 3) d x

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

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

integral of 1.05(x+180)^{0.05}

\int 1.05 (x + 180)^{0.05} d x

integral of (cos(x))/((cos(x)+sin(x)))

\int \frac{cos ( x )}{( cos ( x ) + sin ( x ) )} d x

integral of-5e^{5t}+4

\int - 5 e^{5 t} + 4 d t