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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{4} ln ∣ x ∣ - \frac{1}{2 x} + \frac{1}{4} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

\int \frac{1}{4 ( x + 2 )} d x = \frac{1}{4} ln ∣ x + 2 ∣

= - \frac{1}{4} ln ∣ x ∣ - \frac{1}{2 x} + \frac{1}{4} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} ln ∣ x ∣ - \frac{1}{2 x} + \frac{1}{4} ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

derivative 3x^2+8x+2

d er i v a t i v e 3 x^{2} + 8 x + 2

limit as x approaches 0 of (sqrt(2(x+h(x)))-sqrt(2x))/(h(x))

x \to 0 lim (\frac{2 ( x + h ( x ) ) - 2 x}{h ( x )})

y^{''}+y=0,y(0)=1,y^'(0)=1

y^{^{''}} + y = 0, y (0) = 1, y^{^{'}} (0) = 1

laplacetransform 5t^3

l a pl a ce t r an s f or m 5 t^{3}

derivative of \sqrt[3]{1+x^2}

\frac{d}{d x} (3 1 + x^{2})