de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 1/(x*(x-1))

Lösung

\int \frac{1}{x \cdot ( x - 1 )} d x

Lösung

- ln ∣ x ∣ + ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{x ( x - 1 )} : - \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

(\partial)/(\partial x)((12x)/(sqrt(y+6)))

\frac{\partial}{\partial x} (\frac{12 x}{y + 6})

derivative (ln(8x))/(8x)

d er i v a t i v e \frac{ln ( 8 x )}{8 x}

integral of 3/(e^{sqrt(x))}

\int \frac{3}{e ^{x}} d x

derivative of \sqrt[3]{x}(x^2+4)

\frac{d}{d x} (3 x (x^{2} + 4))

integral of e^{-v}

\int e^{- v} d v