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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

limit as x approaches 0 of sqrt(x^4)

x \to 0 lim (x^{4})

derivative 5-2/t

d er i v a t i v e 5 - \frac{2}{t}

integral of axsin(x)

\int a x sin (x) d x

tangent 5sqrt(x),\at x=16

t an g e n t 5 x, at x = 16

limit as x approaches 1 of x^2+4x

x \to 1 lim (x^{2} + 4 x)