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Beliebt Rechnen >

integral of (3x+11)/(x^2-2x-3)

Lösung

\int \frac{3 x + 11}{x ^{2} - 2 x - 3} d x

Lösung

- 2 ln ∣ x + 1 ∣ + 5 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{3 x + 11}{x ^{2} - 2 x - 3} d x

Ermittle den Partialbruch von

\frac{3 x + 11}{x ^{2} - 2 x - 3} : - \frac{2}{x + 1} + \frac{5}{x - 3}

= \int - \frac{2}{x + 1} + \frac{5}{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 + 1} d x + \int \frac{5}{x - 3} d x

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

\int \frac{5}{x - 3} d x = 5 ln ∣ x - 3 ∣

= - 2 ln ∣ x + 1 ∣ + 5 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= - 2 ln ∣ x + 1 ∣ + 5 ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

integral of (x^3-1)/(x^2-4)

\int \frac{x ^{3} - 1}{x ^{2} - 4} d x

integral of 14sin^2(xco)s^2x

\int 14 sin^{2} (x co) s^{2} x d x

steigung (64,56),(28,33)

s l o p e (64, 56), (28, 33)

limit as x approaches 0-of 1/(x^2+6x)

x \to 0 - lim (\frac{1}{x ^{2} + 6 x})

derivative y=e^{sqrt(x)}(x^2-4)

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