integral of (x+4)(x-5)

Lösung

\int (x + 4) (x - 5) d x

\frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 20 x + C

Schritte zur Lösung

\int (x + 4) (x - 5) d x

Multipliziere aus

(x + 4) (x - 5) : x^{2} - x - 20

= \int x^{2} - x - 20 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 20 d x

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

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

\int 20 d x = 20 x

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 20 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 20 x + C

\frac{d}{d x} (- x^{2} - 1)

d er i v a t i v e (x^{2} - 7 x + 8) 25 - x^{2}

\frac{\partial}{\partial y} (\frac{3 x + 1}{x + 2})

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = 2

\int \frac{1}{1 - 3 v} d v