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Beliebt Rechnen >

integral of (2x^2+x-1)/(2x^3+x^2-5x+2)

Lösung

\int \frac{2 x ^{2} + x - 1}{2 x ^{3} + x ^{2} - 5 x + 2} d x

Lösung

\frac{2}{3} ln ∣ x - 1 ∣ + \frac{1}{3} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{2 x ^{2} + x - 1}{2 x ^{3} + x ^{2} - 5 x + 2} d x

Ermittle den Partialbruch von

\frac{2 x ^{2} + x - 1}{2 x ^{3} + x ^{2} - 5 x + 2} : \frac{2}{3 ( x - 1 )} + \frac{1}{3 ( x + 2 )}

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

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

\int \frac{1}{3 ( x + 2 )} d x = \frac{1}{3} ln ∣ x + 2 ∣

= \frac{2}{3} ln ∣ x - 1 ∣ + \frac{1}{3} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} ln ∣ x - 1 ∣ + \frac{1}{3} ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

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

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

integral of 9/(x^2-16)

\int \frac{9}{x ^{2} - 16} d x

limit as x approaches 2-of x^3

x \to 2 - lim (x^{3})

integral of 3/(5+3x)

\int \frac{3}{5 + 3 x} d x

y^{''}+36y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0