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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{2}{x - 2} d x = 2 ln ∣ x - 2 ∣

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

fläche y=4x^2,x=1,y=0

a re a y = 4 x^{2}, x = 1, y = 0

inverselaplace (2e^{-2s})/(5s^2+45)

in v erse l a pl a ce \frac{2 e ^{- 2 s}}{5 s ^{2} + 45}

derivative y=e^{((3x^2))/2}

d er i v a t i v e y = e^{\frac{( 3 x ^{2} )}{2}}

derivative (x^{63}-1)/(x-1)

d er i v a t i v e \frac{x ^{63} - 1}{x - 1}

derivative of 3/(3x+1)

\frac{d}{d x} (\frac{3}{3 x + 1})