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+1)^2)

Lösung

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

Lösung

ln ∣ x + 1 ∣ + \frac{2}{x + 1} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= ln ∣ x + 1 ∣ + \frac{1}{x + 1} - (- \frac{1}{x + 1})

Vereinfache

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

= ln ∣ x + 1 ∣ + \frac{2}{x + 1}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 1 ∣ + \frac{2}{x + 1} + C

Graph

Beliebte Beispiele

integral of cos^2(t)*sin(t)

\int cos^{2} (t) \cdot sin (t) d t

integral of 64sqrt(64-x^2)

\int 64 64 - x^{2} d x

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

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

integral of (6x^8-2/3 x^5+7x^4+sqrt(3))

\int (6 x^{8} - \frac{2}{3} x^{5} + 7 x^{4} + 3) d x

integral of cos(7x+8)

\int cos (7 x + 8) d x