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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{3 x ^{2} - 7 x - 2}{x ^{3} - x} : \frac{2}{x} + \frac{4}{x + 1} - \frac{3}{x - 1}

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{4}{x + 1} d x = 4 ln ∣ x + 1 ∣

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (1-3x)6x^5

\int (1 - 3 x) 6 x^{5} d x

integral of (1/4 x^3+3x^2-3/5 x+4)

\int (\frac{1}{4} x^{3} + 3 x^{2} - \frac{3}{5} x + 4) d x

integral of-9x^4e^{x^5}

\int - 9 x^{4} e^{x^{5}} d x

integral of 1/((1+sin(x)+cos(x)))

\int \frac{1}{( 1 + sin ( x ) + cos ( x ) )} d x

integral 1/(2x)

in t e g r a l \frac{1}{2 x}