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

Lösung

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

Lösung

x^{2} - ln ∣ x ∣ + ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= x^{2} - ln ∣ x ∣ + ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= x^{2} - ln ∣ x ∣ + ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

limit as x approaches infinity of (3^{x-3})/(2^{n+3)}

x \to \infty lim (\frac{3 ^{x - 3}}{2 ^{n + 3}})

limit as x approaches 2-of x+4

x \to 2 - lim (x + 4)

3y(x^2-1)dx+(x^3+8y-3x)dy=0

3 y (x^{2} - 1) d x + (x^{3} + 8 y - 3 x) d y = 0

steigung y=x^2-5

s l o p e y = x^{2} - 5

derivative f(x)= 1/2 x-1/3

d er i v a t i v e f (x) = \frac{1}{2} x - \frac{1}{3}