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Beliebt Rechnen >

integral of (x-48)/(x^2-x-6)

Lösung

\int \frac{x - 48}{x ^{2} - x - 6} d x

Lösung

10 ln ∣ x + 2 ∣ - 9 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{x - 48}{x ^{2} - x - 6} d x

Ermittle den Partialbruch von

\frac{x - 48}{x ^{2} - x - 6} : \frac{10}{x + 2} - \frac{9}{x - 3}

= \int \frac{10}{x + 2} - \frac{9}{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{10}{x + 2} d x - \int \frac{9}{x - 3} d x

\int \frac{10}{x + 2} d x = 10 ln ∣ x + 2 ∣

\int \frac{9}{x - 3} d x = 9 ln ∣ x - 3 ∣

= 10 ln ∣ x + 2 ∣ - 9 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= 10 ln ∣ x + 2 ∣ - 9 ln ∣ x - 3 ∣ + C

Graph

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