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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 of 2^{2x^2+1}

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

integral of (e^{-x})/(sqrt(1+e^{-x))}

\int \frac{e ^{- x}}{1 + e ^{- x}} d x

integral of (x+6)/(2x^3-8x)

\int \frac{x + 6}{2 x ^{3} - 8 x} d x

integral of 2xsqrt(1-3x^2)

\int 2 x 1 - 3 x^{2} d x

integral of 1/(4v^2-4v+5)

\int \frac{1}{4 v ^{2} - 4 v + 5} d v