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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

\int \frac{4}{x + 2} d x = 4 ln ∣ x + 2 ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 3xe^{x^2}

\int 3 x e^{x^{2}} d x

integral from-2 to 0 of 7x^2+7x

\int_{- 2}^{0} 7 x^{2} + 7 x d x

integral of 1/(1.02^x)

\int \frac{1}{1.0 2 ^{x}} d x

integral of x^4(x^5-1)^{3/4}

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

integral of (sqrt(x-9))/x

\int \frac{x - 9}{x} d x