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Beliebt Rechnen >

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

Lösung

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

Lösung

- ln ∣ x ∣ + ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

(dy)/(dx)=9e^{x-y}

\frac{d y}{d x} = 9 e^{x - y}

derivative f(x)=\sqrt[3]{x^7-4x}

d er i v a t i v e f (x) = 3 x^{7} - 4 x

derivative of sin(3x+cos(4x))

\frac{d}{d x} (sin (3 x) + cos (4 x))

d/(dt)({r}(t)cos(t))

\frac{d}{d t} (r (t) cos (t))

integral of 4/x-(16)/(x^2)

\int \frac{4}{x} - \frac{16}{x ^{2}} d x