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Beliebt Rechnen >

integral of (x-23)/(x^2-x-6)

Lösung

\int \frac{x - 23}{x ^{2} - x - 6} d x

Lösung

5 ln ∣ x + 2 ∣ - 4 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{x - 23}{x ^{2} - x - 6} d x

Ermittle den Partialbruch von

\frac{x - 23}{x ^{2} - x - 6} : \frac{5}{x + 2} - \frac{4}{x - 3}

= \int \frac{5}{x + 2} - \frac{4}{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{5}{x + 2} d x - \int \frac{4}{x - 3} d x

\int \frac{5}{x + 2} d x = 5 ln ∣ x + 2 ∣

\int \frac{4}{x - 3} d x = 4 ln ∣ x - 3 ∣

= 5 ln ∣ x + 2 ∣ - 4 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= 5 ln ∣ x + 2 ∣ - 4 ln ∣ x - 3 ∣ + C

Graph

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\int (8 x + 10) d x

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\int \frac{1}{β ln ^{4} ( β )} d β

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\int \frac{1}{16 x ^{2}} d x