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Beliebt Rechnen >

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

Lösung

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

Lösung

3 ln ∣ x - 2 ∣ + x + C

Schritte zur Lösung

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

\frac{x + 1}{x - 2} = \frac{3}{x - 2} + 1

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

Wende die Summenregel an:

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

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

\int \frac{3}{x - 2} d x = 3 ln ∣ x - 2 ∣

\int 1 d x = x

= 3 ln ∣ x - 2 ∣ + x

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x - 2 ∣ + x + C

Graph

Beliebte Beispiele

sum from n=0 to infinity of 7/(5^n)

n = 0 \sum \infty \frac{7}{5 ^{n}}

integral of-7sec(2x)tan(2x)

\int - 7 sec (2 x) tan (2 x) d x

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

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

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\frac{d}{d x} (e^{3 x - 2})

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\int cot^{3} (5 x) d x