de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{3 x ^{2}}{2} + 3 x + \frac{8}{3} ln ∣ x + 1 ∣ + \frac{34}{3} ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Lange Division

\frac{3 x ^{3} + 5 x}{x ^{2} - x - 2} : 3 x + 3 + \frac{14 x + 6}{x ^{2} - x - 2}

= \int 3 x + 3 + \frac{14 x + 6}{x ^{2} - x - 2} 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 3 x d x + \int 3 d x + \int \frac{14 x + 6}{x ^{2} - x - 2} d x

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 3 d x = 3 x

\int \frac{14 x + 6}{x ^{2} - x - 2} d x = \frac{8}{3} ln ∣ x + 1 ∣ + \frac{34}{3} ln ∣ x - 2 ∣

= \frac{3 x ^{2}}{2} + 3 x + \frac{8}{3} ln ∣ x + 1 ∣ + \frac{34}{3} ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{2}}{2} + 3 x + \frac{8}{3} ln ∣ x + 1 ∣ + \frac{34}{3} ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

limit as x approaches-infinity of arccos(x)

x \to - \infty lim (arccos (x))

integral of (x^2-15L)/(x+7)

\int \frac{x ^{2} - 15 L}{x + 7} d x

derivative (1-3x-x^2)/(x^2-3)

d er i v a t i v e \frac{1 - 3 x - x ^{2}}{x ^{2} - 3}

laplacetransform 2t^3

l a pl a ce t r an s f or m 2 t^{3}

derivative of sin(xln(x^2+1))

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