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^2+5x+4)

Lösung

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

Lösung

- \frac{2}{3} ln ∣ x + 1 ∣ + \frac{5}{3} ln ∣ x + 4 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

= \int - \frac{2}{3 ( x + 1 )} + \frac{5}{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{2}{3 ( x + 1 )} d x + \int \frac{5}{3 ( x + 4 )} d x

\int \frac{2}{3 ( x + 1 )} d x = \frac{2}{3} ln ∣ x + 1 ∣

\int \frac{5}{3 ( x + 4 )} d x = \frac{5}{3} ln ∣ x + 4 ∣

= - \frac{2}{3} ln ∣ x + 1 ∣ + \frac{5}{3} ln ∣ x + 4 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{3} ln ∣ x + 1 ∣ + \frac{5}{3} ln ∣ x + 4 ∣ + C

Graph

Beliebte Beispiele

integral of cos(x)cos^2(4x)

\int cos (x) cos^{2} (4 x) d x

integral of e^x(sin(x)-cos(x))

\int e^{x} (sin (x) - cos (x)) d x

integral of cos(x)(6sin^2(x)-1)

\int cos (x) (6 sin^{2} (x) - 1) d x

integral of (x^2-x-6)/(x^3+x)

\int \frac{x ^{2} - x - 6}{x ^{3} + x} d x

integral of (x^2+3x^{13})^5

\int (x^{2} + 3 x^{13})^{5} d x