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Beliebt Rechnen >

integral of (3x-13)/(x^2+3x-10)

Lösung

\int \frac{3 x - 13}{x ^{2} + 3 x - 10} d x

Lösung

- ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣ + C

Schritte zur Lösung

\int \frac{3 x - 13}{x ^{2} + 3 x - 10} d x

Ermittle den Partialbruch von

\frac{3 x - 13}{x ^{2} + 3 x - 10} : - \frac{1}{x - 2} + \frac{4}{x + 5}

= \int - \frac{1}{x - 2} + \frac{4}{x + 5} 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 - 2} d x + \int \frac{4}{x + 5} d x

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

\int \frac{4}{x + 5} d x = 4 ln ∣ x + 5 ∣

= - ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣ + C

Graph

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