integral of (x-2)(2x+3)

Lösung

\int (x - 2) (2 x + 3) d x

\frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + C

Schritte zur Lösung

\int (x - 2) (2 x + 3) d x

Multipliziere aus

(x - 2) (2 x + 3) : 2 x^{2} - x - 6

= \int 2 x^{2} - x - 6 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 2 x^{2} d x - \int x d x - \int 6 d x

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

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

\int 6 d x = 6 x

= \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + C

x \frac{d y}{d x} = y ln (x y)

\frac{\partial}{\partial x} (sin (y) e^{x})

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

\int_{0}^{2} - 3 x^{3} x^{2} + 4 d x

\int_{0}^{2} \frac{x}{x ^{2} + 1} d x