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Beliebt Rechnen >

integral of (5x+8)/(x^2+2x-8)

Lösung

\int \frac{5 x + 8}{x ^{2} + 2 x - 8} d x

Lösung

3 ln ∣ x - 2 ∣ + 2 ln ∣ x + 4 ∣ + C

Schritte zur Lösung

\int \frac{5 x + 8}{x ^{2} + 2 x - 8} d x

Ermittle den Partialbruch von

\frac{5 x + 8}{x ^{2} + 2 x - 8} : \frac{3}{x - 2} + \frac{2}{x + 4}

= \int \frac{3}{x - 2} + \frac{2}{x + 4} 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{3}{x - 2} d x + \int \frac{2}{x + 4} d x

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

\int \frac{2}{x + 4} d x = 2 ln ∣ x + 4 ∣

= 3 ln ∣ x - 2 ∣ + 2 ln ∣ x + 4 ∣

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x - 2 ∣ + 2 ln ∣ x + 4 ∣ + C

Graph

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