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Beliebt Rechnen >

integral of (x-2)/(x-3)

Lösung

\int \frac{x - 2}{x - 3} d x

Lösung

ln ∣ x - 3 ∣ + x + C

Schritte zur Lösung

\int \frac{x - 2}{x - 3} d x

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

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

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

\int 1 d x = x

= ln ∣ x - 3 ∣ + x

Füge eine Konstante zur Lösung hinzu

= ln ∣ x - 3 ∣ + x + C

Graph

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