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Beliebt Rechnen >

integral of (3x-2)/(x+1)

Lösung

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

Lösung

3 (x + 1) - 5 ln ∣ x + 1 ∣ + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{3 u - 5}{u} d u

Multipliziere aus

\frac{3 u - 5}{u} : 3 - \frac{5}{u}

= \int 3 - \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 3 d u - \int \frac{5}{u} d u

\int 3 d u = 3 u

\int \frac{5}{u} d u = 5 ln ∣ u ∣

= 3 u - 5 ln ∣ u ∣

Setze in

u = x + 1

ein

= 3 (x + 1) - 5 ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 3 (x + 1) - 5 ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

limit as x approaches-3 of |-x-1|

x \to - 3 lim (∣ - x - 1 ∣)

integral of 1/((x-3)(x-1))

\int \frac{1}{( x - 3 ) ( x - 1 )} d x

derivative 6/5-6/5 e^{-20t}

d er i v a t i v e \frac{6}{5} - \frac{6}{5} e^{- 20 t}

longdivision (x^2+1)/(x^2-4)

l o n g d i v i s i o n \frac{x ^{2} + 1}{x ^{2} - 4}

\frac{d y}{d x} = 4 - y