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Beliebt Rechnen >

integral of (x-1)/(x^2+3x+2)

Lösung

\int \frac{x - 1}{x ^{2} + 3 x + 2} d x

Lösung

- 2 ln ∣ x + 1 ∣ + 3 ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{x - 1}{x ^{2} + 3 x + 2} d x

Ermittle den Partialbruch von

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

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

\int \frac{2}{x + 1} d x = 2 ln ∣ x + 1 ∣

\int \frac{3}{x + 2} d x = 3 ln ∣ x + 2 ∣

= - 2 ln ∣ x + 1 ∣ + 3 ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= - 2 ln ∣ x + 1 ∣ + 3 ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

(dy)/(dx)=(3y)^{1/2}e^{x+10}

\frac{d y}{d x} = (3 y)^{\frac{1}{2}} e^{x + 10}

integral from-1 to 1 of (x^3-9x)

\int_{- 1}^{1} (x^{3} - 9 x) d x

limit as x approaches 0 of 1/x sin(x/3)

x \to 0 lim (\frac{1}{x} sin (\frac{x}{3}))

\frac{d y}{d x} + 7 y = 5

derivative-2x^2(x+4)

d er i v a t i v e - 2 x^{2} (x + 4)