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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

y^{^{''}} - y^{^{'}} = 1

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