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

Lösung

\int (x - 1) (x + 2) d x

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

Schritte zur Lösung

\int (x - 1) (x + 2) d x

Multipliziere aus

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

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

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

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

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e f (x) = 5 x^{\frac{4}{5}} - 2 x^{\frac{2}{7}}

d er i v a t i v e \frac{1}{x + 5}

\int t (2 t - 3 t) d t

\frac{\partial}{\partial z} (- x y z^{2})

\int x \cdot 4 x^{11} d x