de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (2x-1)/((x-1)(x-2)(2x-3))

Lösung

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

Lösung

ln ∣ x - 1 ∣ + 3 ln ∣ x - 2 ∣ - 4 ln ∣ 2 x - 3 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x - 1} d x = ln ∣ x - 1 ∣

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

\int \frac{8}{2 x - 3} d x = 4 ln ∣ 2 x - 3 ∣

= ln ∣ x - 1 ∣ + 3 ln ∣ x - 2 ∣ - 4 ln ∣ 2 x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x - 1 ∣ + 3 ln ∣ x - 2 ∣ - 4 ln ∣ 2 x - 3 ∣ + C

Graph

Beliebte Beispiele

derivative of e^{-x}cos(y)

\frac{d}{d x} (e^{- x} cos (y))

derivative of (1+x^3^5)

\frac{d}{d x} ((1 + x^{3})^{5})

(\partial)/(\partial y)(e^ysin(x)y)

\frac{\partial}{\partial y} (e^{y} sin (x) y)

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

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

(dy)/(dt)=-6/((2000+6t))

\frac{d y}{d t} = - \frac{6}{( 2000 + 6 t )}