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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x ∣ - ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

derivative derivative of x/a

d er i v a t i v e \frac{d}{d x} (\frac{x}{a})

derivative derivative of 2e^{-2x}

d er i v a t i v e \frac{d}{d x} (2 e^{- 2 x})

derivative d/(dy)(y^2)

d er i v a t i v e \frac{d}{d y} (y^{2})

integral (-1)/((e^x))

in t e g r a l \frac{- 1}{( e ^{x} )}

derivative of y=4x

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