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/((x+2)(x-4))

Lösung

\int \frac{x}{( x + 2 ) ( x - 4 )} d x

Lösung

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

Schritte zur Lösung

\int \frac{x}{( x + 2 ) ( x - 4 )} d x

Ermittle den Partialbruch von

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

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

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

\int \frac{2}{3 ( x - 4 )} d x = \frac{2}{3} ln ∣ x - 4 ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of sec(2x)*tan(2x)

\int sec (2 x) \cdot tan (2 x) d x

integral of (2x-3)/(x^2+4)

\int \frac{2 x - 3}{x ^{2} + 4} d x

sum from n=1 to infinity of (2n)/(n^2)

n = 1 \sum \infty \frac{2 n}{n ^{2}}

derivative y=-8xln(6x+5)

d er i v a t i v e y = - 8 x ln (6 x + 5)

tangent y=(x^3-16x)^{12},(4,0)

t an g e n t y = (x^{3} - 16 x)^{12}, (4, 0)