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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (2x^2)/(1-2x^3)

\int \frac{2 x ^{2}}{1 - 2 x ^{3}} d x

tangent f(x)=(12x-3)^{1/2},\at x=1

t an g e n t f (x) = (12 x - 3)^{\frac{1}{2}}, at x = 1

limit as x approaches-infinity of e^x-x

x \to - \infty lim (e^{x} - x)

derivative of cot^2(5x)

\frac{d}{d x} (cot^{2} (5 x))

derivative of cos(3sin(x))

\frac{d}{d x} (cos (3 sin (x)))