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-3)/(x^2+5x+6)

Lösung

\int \frac{x - 3}{x ^{2} + 5 x + 6} d x

Lösung

- 5 ln ∣ x + 2 ∣ + 6 ln ∣ x + 3 ∣ + C

Schritte zur Lösung

\int \frac{x - 3}{x ^{2} + 5 x + 6} d x

Ermittle den Partialbruch von

\frac{x - 3}{x ^{2} + 5 x + 6} : - \frac{5}{x + 2} + \frac{6}{x + 3}

= \int - \frac{5}{x + 2} + \frac{6}{x + 3} 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{5}{x + 2} d x + \int \frac{6}{x + 3} d x

\int \frac{5}{x + 2} d x = 5 ln ∣ x + 2 ∣

\int \frac{6}{x + 3} d x = 6 ln ∣ x + 3 ∣

= - 5 ln ∣ x + 2 ∣ + 6 ln ∣ x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= - 5 ln ∣ x + 2 ∣ + 6 ln ∣ x + 3 ∣ + C

Graph

Beliebte Beispiele

integral of (e^y)/(e^y-1)

\int \frac{e ^{y}}{e ^{y} - 1} d y

integral of 1/(x(7+ln(x^2)))

\int \frac{1}{x ( 7 + ln ( x ^{2} ) )} d x

integral of (ln(xe^x))/x

\int \frac{ln ( x e ^{x} )}{x} d x

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

\int \frac{3}{sec ^{2} ( 5 x )} d x

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

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