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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

derivative (t^2)/(t-2)

d er i v a t i v e \frac{t ^{2}}{t - 2}

integral of (6x^5+7x)

\int (6 x^{5} + 7 x) d x

(dy)/(dx)=(y^2)/(e^x),y(0)=-2

\frac{d y}{d x} = \frac{y ^{2}}{e ^{x}}, y (0) = - 2

limit as x approaches infinity of (sqrt(x))/(ln(x))

x \to \infty lim (\frac{x}{ln ( x )})

derivative of (x/2+1^3)

\frac{d}{d x} ((\frac{x}{2} + 1)^{3})