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Beliebt Rechnen >

integral ((x+7))/((x+9))

Lösung

integral

\frac{( x + 7 )}{( x + 9 )}

Lösung

- 2 ln ∣ x + 9 ∣ + x + C

Schritte zur Lösung

\int \frac{x + 7}{x + 9} d x

\frac{x + 7}{x + 9} = - \frac{2}{x + 9} + 1

= \int - \frac{2}{x + 9} + 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}{x + 9} d x + \int 1 d x

\int \frac{2}{x + 9} d x = 2 ln ∣ x + 9 ∣

\int 1 d x = x

= - 2 ln ∣ x + 9 ∣ + x

Füge eine Konstante zur Lösung hinzu

= - 2 ln ∣ x + 9 ∣ + x + C

Graph

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