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Beliebt Rechnen >

integral of (1-2x)/((x+1)(x-5))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

\int \frac{3}{2 ( x - 5 )} d x = \frac{3}{2} ln ∣ x - 5 ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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