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Beliebt Rechnen >

integral of (4x-2)/(x(x+1)(x-2))

Lösung

\int \frac{4 x - 2}{x ( x + 1 ) ( x - 2 )} d x

Lösung

ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{4 x - 2}{x ( x + 1 ) ( x - 2 )} d x

Ermittle den Partialbruch von

\frac{4 x - 2}{x ( x + 1 ) ( x - 2 )} : \frac{1}{x} - \frac{2}{x + 1} + \frac{1}{x - 2}

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

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

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

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

integral from 4 to infinity of e^{-7x}

\int_{4}^{\infty} e^{- 7 x} d x

(dy}{4y}=\frac{dx)/x

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

derivative f(x)=6x^2tan(x)

d er i v a t i v e f (x) = 6 x^{2} tan (x)

derivative of ln|x-3|

\frac{d}{d x} (ln ∣ x - 3 ∣)

(d^2)/(dx^2)(sqrt(x)+\sqrt[5]{x})

\frac{d ^{2}}{d x ^{2}} (x + 5 x)