de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

- ln ∣ x ∣ + ln ∣ x + 1 ∣ - \frac{2}{x + 1} + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x - 1}{x ( x + 1 ) ^{2}} : - \frac{1}{x} + \frac{1}{x + 1} + \frac{2}{( x + 1 ) ^{2}}

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

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

= - ln ∣ x ∣ + ln ∣ x + 1 ∣ - \frac{2}{x + 1}

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x ∣ + ln ∣ x + 1 ∣ - \frac{2}{x + 1} + C

Graph

Beliebte Beispiele

integral of (x^5)/(\sqrt[7]{ax^6+2)}

\int \frac{x ^{5}}{7 a x ^{6} + 2} d x

integral of (y-8)/(y^2-y-6)

\int \frac{y - 8}{y ^{2} - y - 6} d y

integral of cot(x)sin(x)

\int cot (x) sin (x) d x

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

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

integral of (3y)/(sqrt(2y^2+5y))

\int \frac{3 y}{2 y ^{2} + 5 y} d y