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Beliebt Rechnen >

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

Lösung

\int \frac{2 x + 1}{x + 2} d x

Lösung

2 (x + 2) - 3 ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{2 x + 1}{x + 2} d x

Wende U-Substitution an

= \int \frac{2 u - 3}{u} d u

Multipliziere aus

\frac{2 u - 3}{u} : 2 - \frac{3}{u}

= \int 2 - \frac{3}{u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 d u - \int \frac{3}{u} d u

\int 2 d u = 2 u

\int \frac{3}{u} d u = 3 ln ∣ u ∣

= 2 u - 3 ln ∣ u ∣

Setze in

u = x + 2

ein

= 2 (x + 2) - 3 ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= 2 (x + 2) - 3 ln ∣ x + 2 ∣ + C

Graph

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