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Beliebt Rechnen >

integral of 1/(x^2-7x+10)

Lösung

\int \frac{1}{x ^{2} - 7 x + 10} d x

Lösung

- \frac{1}{3} ln ∣ x - 2 ∣ + \frac{1}{3} ln ∣ x - 5 ∣ + C

Schritte zur Lösung

\int \frac{1}{x ^{2} - 7 x + 10} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} - 7 x + 10} : - \frac{1}{3 ( x - 2 )} + \frac{1}{3 ( x - 5 )}

= \int - \frac{1}{3 ( x - 2 )} + \frac{1}{3 ( 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}{3 ( x - 2 )} d x + \int \frac{1}{3 ( x - 5 )} d x

\int \frac{1}{3 ( x - 2 )} d x = \frac{1}{3} ln ∣ x - 2 ∣

\int \frac{1}{3 ( x - 5 )} d x = \frac{1}{3} ln ∣ x - 5 ∣

= - \frac{1}{3} ln ∣ x - 2 ∣ + \frac{1}{3} ln ∣ x - 5 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} ln ∣ x - 2 ∣ + \frac{1}{3} ln ∣ x - 5 ∣ + C

Graph

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