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Beliebt Rechnen >

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

Lösung

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

Lösung

2 x - 2 + 3 ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{2 x + 1}{x - 1} : \frac{2 x}{x - 1} + \frac{1}{x - 1}

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

\int \frac{2 x}{x - 1} d x = 2 (x - 1 + ln ∣ x - 1 ∣)

\int \frac{1}{x - 1} d x = ln ∣ x - 1 ∣

= 2 (x - 1 + ln ∣ x - 1 ∣) + ln ∣ x - 1 ∣

Vereinfache

2 (x - 1 + ln ∣ x - 1 ∣) + ln ∣ x - 1 ∣ : 2 x - 2 + 3 ln ∣ x - 1 ∣

= 2 x - 2 + 3 ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= 2 x - 2 + 3 ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

limit as x approaches infinity of 4^x

x \to \infty lim (4^{x})

(dy)/(dx)+(3/x)y=-x-5

\frac{d y}{d x} + (\frac{3}{x}) y = - x - 5

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x \to 0 lim (\frac{sin ( 1 )}{1})

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