de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{- x - 2}{4 x ^{2}} d x = \frac{1}{4} (- ln ∣ x ∣ + \frac{2}{x})

\int \frac{1}{4 ( x - 2 )} d x = \frac{1}{4} ln ∣ x - 2 ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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

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

integral of (2x+2)/(x^2+2x+1)

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

integral of 5^{x^2}*x

\int 5^{x^{2}} \cdot x d x

integral of 4/(x^2)sec(1/x)tan(1/x)

\int \frac{4}{x ^{2}} sec (\frac{1}{x}) tan (\frac{1}{x}) d x

integral of (2u)/(sqrt(-4u^2+9))

\int \frac{2 u}{- 4 u ^{2} + 9} d u