integral of x^2(x-2)

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

n = 0 \sum \infty \frac{n !}{10 3 ^{n}}

\frac{\partial}{\partial y} (x^{2} + 2 x y^{2} + 2 y^{2})

d er i v a t i v e f (x) = x^{3} - \frac{3}{2} x^{2}

a re a y = 2 - ∣ x ∣, y = x^{2}

d er i v a t i v e \frac{1}{x} + 6