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Beliebt Rechnen >

integral of 1/(x^2-2x-8)

Lösung

\int \frac{1}{x ^{2} - 2 x - 8} d x

Lösung

- \frac{1}{6} ln ∣ x + 2 ∣ + \frac{1}{6} ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{1}{x ^{2} - 2 x - 8} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} - 2 x - 8} : - \frac{1}{6 ( x + 2 )} + \frac{1}{6 ( x - 4 )}

= \int - \frac{1}{6 ( x + 2 )} + \frac{1}{6 ( 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}{6 ( x + 2 )} d x + \int \frac{1}{6 ( x - 4 )} d x

\int \frac{1}{6 ( x + 2 )} d x = \frac{1}{6} ln ∣ x + 2 ∣

\int \frac{1}{6 ( x - 4 )} d x = \frac{1}{6} ln ∣ x - 4 ∣

= - \frac{1}{6} ln ∣ x + 2 ∣ + \frac{1}{6} ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{6} ln ∣ x + 2 ∣ + \frac{1}{6} ln ∣ x - 4 ∣ + C

Graph

Beliebte Beispiele

derivative of ln(1/(sqrt(6x)))

\frac{d}{d x} (ln (\frac{1}{6 x}))

derivative f(x)=7tan(x^4)

d er i v a t i v e f (x) = 7 tan (x^{4})

derivative 70pit+35cos((-2pit-pi)/2)

d er i v a t i v e 70 π t + 35 cos (\frac{- 2 π t - π}{2})

integral of sin(3x)cos(7x)

\int sin (3 x) cos (7 x) d x

derivative of sin(5x-2)

\frac{d}{d x} (sin (5 x - 2))