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

Lösung

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

- 6 ln ∣ x + 3 ∣ + x + C

Schritte zur Lösung

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

\frac{x - 3}{x + 3} = - \frac{6}{x + 3} + 1

= \int - \frac{6}{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{6}{x + 3} d x + \int 1 d x

\int \frac{6}{x + 3} d x = 6 ln ∣ x + 3 ∣

\int 1 d x = x

= - 6 ln ∣ x + 3 ∣ + x

Füge eine Konstante zur Lösung hinzu

= - 6 ln ∣ x + 3 ∣ + x + C

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