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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x ^{2} - 4 x + 3}{x ^{3} + 2 x ^{2} + x} : \frac{3}{x} - \frac{2}{x + 1} - \frac{8}{( x + 1 ) ^{2}}

= \int \frac{3}{x} - \frac{2}{x + 1} - \frac{8}{( x + 1 ) ^{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 \frac{3}{x} d x - \int \frac{2}{x + 1} d x - \int \frac{8}{( x + 1 ) ^{2}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

\int \frac{8}{( x + 1 ) ^{2}} d x = - \frac{8}{x + 1}

= 3 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ - (- \frac{8}{x + 1})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

limit as z approaches 2 of sqrt(7z^2+14z-7)

z \to 2 lim (7 z^{2} + 14 z - 7)

integral of 1/((x^2+3x-4))

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

inverselaplace 1/(s^2(s+1))

in v erse l a pl a ce \frac{1}{s ^{2} ( s + 1 )}

integral of (x^3-10x-3)

\int (x^{3} - 10 x - 3) d x

derivative a^3+cos^3(x)

d er i v a t i v e a^{3} + cos^{3} (x)