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Beliebt Rechnen >

integral of (x-6)/(x^2(x+2))

Lösung

\int \frac{x - 6}{x ^{2} ( x + 2 )} d x

Lösung

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

Schritte zur Lösung

\int \frac{x - 6}{x ^{2} ( x + 2 )} d x

Ermittle den Partialbruch von

\frac{x - 6}{x ^{2} ( x + 2 )} : \frac{2}{x} - \frac{3}{x ^{2}} - \frac{2}{x + 2}

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of t^2sin(Bt)

\int t^{2} sin (Bt) d t

integral of (x^7)/(x^8)

\int \frac{x ^{7}}{x ^{8}} d x

integral of (4x-11)/((x-5)(2x-1))

\int \frac{4 x - 11}{( x - 5 ) ( 2 x - 1 )} d x

integral of tan^2(3-2x)

\int tan^{2} (3 - 2 x) d x

integral of (cos(5/2)x)^4

\int (cos (\frac{5}{2}) x)^{4} d x