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Beliebt Rechnen >

integral of y/(y+2)

Lösung

\int \frac{y}{y + 2} d y

Lösung

y + 2 - 2 ln ∣ y + 2 ∣ + C

Schritte zur Lösung

\int \frac{y}{y + 2} d y

Wende U-Substitution an

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

Multipliziere aus

\frac{u - 2}{u} : 1 - \frac{2}{u}

= \int 1 - \frac{2}{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{2}{u} d u

\int 1 d u = u

\int \frac{2}{u} d u = 2 ln ∣ u ∣

= u - 2 ln ∣ u ∣

Setze in

u = y + 2

ein

= y + 2 - 2 ln ∣ y + 2 ∣

Füge eine Konstante zur Lösung hinzu

= y + 2 - 2 ln ∣ y + 2 ∣ + C

Graph

Beliebte Beispiele

derivative of (e^x/(6+e^x))

\frac{d}{d x} (\frac{e ^{x}}{6 + e ^{x}})

derivative of (64x/(x^2+64))

\frac{d}{d x} (\frac{64 x}{x ^{2} + 64})

integral of 4(1+tan^2(x))

\int 4 (1 + tan^{2} (x)) d x

(dy)/(dx)=100-y

\frac{d y}{d x} = 100 - y

limit as x approaches infinity of (1+1/(2x+1))^{sqrt(x^{2-3)}}

x \to \infty lim ((1 + \frac{1}{2 x + 1})^{x^{2 - 3}})