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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

t^2y^{''}+5ty^'+4y=0

t^{2} y^{^{''}} + 5 t y^{^{'}} + 4 y = 0

limit as x approaches 1+of (x-1)/(x-1)

x \to 1 + lim (\frac{x - 1}{x - 1})

limit as x approaches 0 of (2sin(x/2))/x

x \to 0 lim (\frac{2 sin ( \frac{x}{2} )}{x})

derivative f(x)=(4/5 x)^4

d er i v a t i v e f (x) = (\frac{4}{5} x)^{4}

(dy)/(dx)=(xe^{x^2})

\frac{d y}{d x} = (x e^{x^{2}})