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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

y^'+x/(x^2+1)y=-4x

y^{^{'}} + \frac{x}{x ^{2} + 1} y = - 4 x

tangent y=(((x+2))/((x-3)))^2,\at x=4

t an g e n t y = (\frac{( x + 2 )}{( x - 3 )})^{2}, at x = 4

derivative of a(e^x+e^xx)

\frac{d}{d x} (a (e^{x} + e^{x} x))

integral of 1/6 x^2

\int \frac{1}{6} x^{2} d x

integral from 0 to 4 of 8e^{-3x}

\int_{0}^{4} 8 e^{- 3 x} d x