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

Lösung

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

Lösung

\frac{x ^{2}}{2} + x - \frac{9}{5} ln ∣ x + 2 ∣ + \frac{14}{5} ln ∣ x - 3 ∣ + C

Schritte zur Lösung

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

Lange Division

\frac{x ^{3} - 6 x + 5}{x ^{2} - x - 6} : x + 1 + \frac{x + 11}{x ^{2} - x - 6}

= \int x + 1 + \frac{x + 11}{x ^{2} - x - 6} 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 x d x + \int 1 d x + \int \frac{x + 11}{x ^{2} - x - 6} d x

\int x d x = \frac{x ^{2}}{2}

\int 1 d x = x

\int \frac{x + 11}{x ^{2} - x - 6} d x = - \frac{9}{5} ln ∣ x + 2 ∣ + \frac{14}{5} ln ∣ x - 3 ∣

= \frac{x ^{2}}{2} + x - \frac{9}{5} ln ∣ x + 2 ∣ + \frac{14}{5} ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + x - \frac{9}{5} ln ∣ x + 2 ∣ + \frac{14}{5} ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

integral of (cos(x))/(8sin^2(x)+9sin(x))

\int \frac{cos ( x )}{8 sin ^{2} ( x ) + 9 sin ( x )} d x

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

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

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