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Beliebt Rechnen >

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

Lösung

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

Lösung

2 ln ∣ x + 2 ∣ - ln ∣ x + 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

= 2 ln ∣ x + 2 ∣ - ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x + 2 ∣ - ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

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

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

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

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

integral of (x+sqrt(1-x^2))^2

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

integral of (x^3)/(5+3x^4)

\int \frac{x ^{3}}{5 + 3 x ^{4}} d x

integral of e^x(2+3e^x)^4

\int e^{x} (2 + 3 e^{x})^{4} d x