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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (7x+3)/(x^2+3x-4)

\int \frac{7 x + 3}{x ^{2} + 3 x - 4} d x

integral of xsin(1nx)

\int x sin (1 n x) d x

integral of (e^{5sqrt(x)})/(sqrt(x))

\int \frac{e ^{5 x}}{x} d x

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

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

integral of (x^2)/((x^2-1)^{5/2)}

\int \frac{x ^{2}}{( x ^{2} - 1 ) ^{\frac{5}{2}}} d x