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+1/(x-1)

Lösung

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

Lösung

x + ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

\int 1 d x = x

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

= x + ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= x + ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

integral of 1/(x^2+4x+29)

\int \frac{1}{x ^{2} + 4 x + 29} d x

t a y l or x^{\frac{1}{3}}

derivative of-e^x(x+6)

\frac{d}{d x} (- e^{x} (x + 6))

limit as x approaches 3+of (4-x)/(9-x^2)

x \to 3 + lim (\frac{4 - x}{9 - x ^{2}})

integral of (sin(3x))/(3+3cos(3x))

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