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Beliebt Rechnen >

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

Lösung

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

Lösung

3 ln ∣ x + 1 ∣ - 2 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= ln ∣ x + 1 ∣ - 2 (ln ∣ x ∣ - ln ∣ x + 1 ∣)

Vereinfache

ln ∣ x + 1 ∣ - 2 (ln ∣ x ∣ - ln ∣ x + 1 ∣) : 3 ln ∣ x + 1 ∣ - 2 ln ∣ x ∣

= 3 ln ∣ x + 1 ∣ - 2 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x + 1 ∣ - 2 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

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