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^2+2x+1)

Lösung

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

Lösung

- \frac{2}{x + 1} - ln ∣ x + 1 ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Vereinfache

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

= - \frac{2}{x + 1} - ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (sin(x))/((4+cos(x))^{3/2)}

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

integral of 3/(2x+5)

\int \frac{3}{2 x + 5} d x

integral of ((csc(x))/(1+cot(x)))^2

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

integral of 1/(49^2+9x-6)

\int \frac{1}{4 9 ^{2} + 9 x - 6} d x

integral of (x^2+2)/(e^x)

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