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Beliebt Rechnen >

integral of ((x+3))/((x+4))

Lösung

\int \frac{( x + 3 )}{( x + 4 )} d x

Lösung

- ln ∣ x + 4 ∣ + x + C

Schritte zur Lösung

\int \frac{x + 3}{x + 4} d x

\frac{x + 3}{x + 4} = - \frac{1}{x + 4} + 1

= \int - \frac{1}{x + 4} + 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 + 4} d x + \int 1 d x

\int \frac{1}{x + 4} d x = ln ∣ x + 4 ∣

\int 1 d x = x

= - ln ∣ x + 4 ∣ + x

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x + 4 ∣ + x + C

Graph

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