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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 1/(sqrt(25+y^2))

\int \frac{1}{25 + y ^{2}} d y

integral of (30)/(0.06t+5)

\int \frac{30}{0.06 t + 5} d t

integral of 3x^2+e^x-6

\int 3 x^{2} + e^{x} - 6 d x

integral of (x-2)e^{x^2-4x}

\int (x - 2) e^{x^{2} - 4 x} d x

integral of (4-x^2)/(x^2)

\int \frac{4 - x ^{2}}{x ^{2}} d x