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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{5} ln ∣ x + 4 ∣ + \frac{1}{5} ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{( x + 4 ) ( x - 1 )} : - \frac{1}{5 ( x + 4 )} + \frac{1}{5 ( x - 1 )}

= \int - \frac{1}{5 ( x + 4 )} + \frac{1}{5 ( x - 1 )} 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}{5 ( x + 4 )} d x + \int \frac{1}{5 ( x - 1 )} d x

\int \frac{1}{5 ( x + 4 )} d x = \frac{1}{5} ln ∣ x + 4 ∣

\int \frac{1}{5 ( x - 1 )} d x = \frac{1}{5} ln ∣ x - 1 ∣

= - \frac{1}{5} ln ∣ x + 4 ∣ + \frac{1}{5} ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} ln ∣ x + 4 ∣ + \frac{1}{5} ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

fläche y=e^x,y=e^{-3x},x=ln(5)

a re a y = e^{x}, y = e^{- 3 x}, x = ln (5)

integral of sqrt(x^2+2x+5)

\int x^{2} + 2 x + 5 d x

tangent f(x)=x^2+8,(4,24)

t an g e n t f (x) = x^{2} + 8, (4, 24)

derivative of (3-2x/(3+2x))

\frac{d}{d x} (\frac{3 - 2 x}{3 + 2 x})

integral of x^4sin(3x)

\int x^{4} sin (3 x) d x