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Beliebt Rechnen >

integral of-1/(x+8)+9/(x-4)

Lösung

\int - \frac{1}{x + 8} + \frac{9}{x - 4} d x

Lösung

- ln ∣ x + 8 ∣ + 9 ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int - \frac{1}{x + 8} + \frac{9}{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{1}{x + 8} d x + \int \frac{9}{x - 4} d x

\int \frac{1}{x + 8} d x = ln ∣ x + 8 ∣

\int \frac{9}{x - 4} d x = 9 ln ∣ x - 4 ∣

= - ln ∣ x + 8 ∣ + 9 ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x + 8 ∣ + 9 ln ∣ x - 4 ∣ + C

Graph

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