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+2)/(x^2+2x)

Lösung

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

Lösung

- 2 ln ∣ x + 2 ∣ + ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{- x + 2}{x ^{2} + 2 x} : - \frac{x}{x ^{2} + 2 x} + \frac{2}{x ^{2} + 2 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{x}{x ^{2} + 2 x} d x + \int \frac{2}{x ^{2} + 2 x} d x

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

\int \frac{2}{x ^{2} + 2 x} d x = - ln ∣ x + 2 ∣ + ln ∣ x ∣

= - ln ∣ x + 2 ∣ - ln ∣ x + 2 ∣ + ln ∣ x ∣

Vereinfache

= - 2 ln ∣ x + 2 ∣ + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - 2 ln ∣ x + 2 ∣ + ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (2x+3)/(x^2+4)

\int \frac{2 x + 3}{x ^{2} + 4} d x

integral of-6e^{2sin(x)}cos(x)

\int - 6 e^{2 s i n (x)} cos (x) d x

integral of (2^x-3^x)/(5^x)

\int \frac{2 ^{x} - 3 ^{x}}{5 ^{x}} d x

integral of 2x^3\sqrt[5]{3x^4+7}

\int 2 x^{3} 5 3 x^{4} + 7 d x

integral of (y+3)/(y-2)

\int \frac{y + 3}{y - 2} d y