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Beliebt Rechnen >

integral of (3x-4)/(x^2-x-6)

Lösung

\int \frac{3 x - 4}{x ^{2} - x - 6} d x

Lösung

2 ln ∣ x + 2 ∣ + ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{3 x - 4}{x ^{2} - x - 6} d x

Ermittle den Partialbruch von

\frac{3 x - 4}{x ^{2} - x - 6} : \frac{2}{x + 2} + \frac{1}{x - 3}

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

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

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

= 2 ln ∣ x + 2 ∣ + ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x + 2 ∣ + ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

derivative of 6sqrt(x)-3x

\frac{d}{d x} (6 x - 3 x)

limit as x approaches 5-of cx^2+2x

x \to 5 - lim (c x^{2} + 2 x)

fläche y=(x^2)/2-4x+6,y= x/2-1

a re a y = \frac{x ^{2}}{2} - 4 x + 6, y = \frac{x}{2} - 1

implicit x^{1/2}+y^{1/2}=9

im pl i c i t x^{\frac{1}{2}} + y^{\frac{1}{2}} = 9

derivative of (x+9/(x-9))

\frac{d}{d x} (\frac{x + 9}{x - 9})