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^2+5x+4)

Lösung

\int \frac{1}{x ^{2} + 5 x + 4} d x

Lösung

\frac{1}{3} ln ∣ x + 1 ∣ - \frac{1}{3} ln ∣ x + 4 ∣ + C

Schritte zur Lösung

\int \frac{1}{x ^{2} + 5 x + 4} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} + 5 x + 4} : \frac{1}{3 ( x + 1 )} - \frac{1}{3 ( x + 4 )}

= \int \frac{1}{3 ( x + 1 )} - \frac{1}{3 ( x + 4 )} 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}{3 ( x + 1 )} d x - \int \frac{1}{3 ( x + 4 )} d x

\int \frac{1}{3 ( x + 1 )} d x = \frac{1}{3} ln ∣ x + 1 ∣

\int \frac{1}{3 ( x + 4 )} d x = \frac{1}{3} ln ∣ x + 4 ∣

= \frac{1}{3} ln ∣ x + 1 ∣ - \frac{1}{3} ln ∣ x + 4 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} ln ∣ x + 1 ∣ - \frac{1}{3} ln ∣ x + 4 ∣ + C

Graph

Beliebte Beispiele

limit as x approaches 5 of sqrt(x-9)

x \to 5 lim (x - 9)

partialfraction x/(2x+1)

p a r t ia l f r a c t i o n \frac{x}{2 x + 1}

integral of (log_{10}(x^2))/x

\int \frac{lo g _{10} ( x ^{2} )}{x} d x

integral of 4x^2-2*x

\int 4 x^{2} - 2 \cdot x d x

integral from 0 to 7 of pi(x+1)^2

\int_{0}^{7} π (x + 1)^{2} d x