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Beliebt Rechnen >

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

Lösung

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

Lösung

x + 2 - 5 ln ∣ x + 2 ∣ + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u - 5}{u} d u

Multipliziere aus

\frac{u - 5}{u} : 1 - \frac{5}{u}

= \int 1 - \frac{5}{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 1 d u - \int \frac{5}{u} d u

\int 1 d u = u

\int \frac{5}{u} d u = 5 ln ∣ u ∣

= u - 5 ln ∣ u ∣

Setze in

u = x + 2

ein

= x + 2 - 5 ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= x + 2 - 5 ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

integral of ln(x^2+1)x

\int ln (x^{2} + 1) x d x

integral of 6x^24^{x^3}

\int 6 x^{2} 4^{x^{3}} d x

integral of (sqrt(x)+1)(\sqrt[3]{x}-1)

\int (x + 1) (3 x - 1) d x

integral of (x^2-5)/(x+2)

\int \frac{x ^{2} - 5}{x + 2} d x

integral of 1/(x^{1/3)+x^{2/3}}

\int \frac{1}{x ^{\frac{1}{3}} + x ^{\frac{2}{3}}} d x