de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

\int \frac{1}{x - x ^{2} + 2} d x

Lösung

\frac{1}{3} ln ∣ x + 1 ∣ - \frac{1}{3} ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{1}{x - x ^{2} + 2} d x

Ermittle den Partialbruch von

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

= \int \frac{1}{3 ( x + 1 )} - \frac{1}{3 ( 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 \frac{1}{3 ( x + 1 )} d x - \int \frac{1}{3 ( x - 2 )} d x

\int \frac{1}{3 ( x + 1 )} d x = \frac{1}{3} ln ∣ x + 1 ∣

\int \frac{1}{3 ( x - 2 )} d x = \frac{1}{3} ln ∣ x - 2 ∣

= \frac{1}{3} ln ∣ x + 1 ∣ - \frac{1}{3} ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} ln ∣ x + 1 ∣ - \frac{1}{3} ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

integral of (2+x)/x

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

derivative of e^{aarccos(x})

\frac{d}{d x} (e^{a a r c c o s (x)})

fläche 2cos(9x),2-2cos(9x),[0, pi/9 ]

a re a 2 cos (9 x), 2 - 2 cos (9 x), [0, \frac{π}{9}]

integral of 6arctan(sqrt(x))

\int 6 arctan (x) d x

limit as x approaches 8+of 1/(|8-x|)

x \to 8 + lim (\frac{1}{∣ 8 - x ∣})