integral of (x-5)/(x^2-x-2)

Lösung

\int \frac{x - 5}{x ^{2} - x - 2} d x

2 ln ∣ x + 1 ∣ - ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{x - 5}{x ^{2} - x - 2} d x

Ermittle den Partialbruch von

\frac{x - 5}{x ^{2} - x - 2} : \frac{2}{x + 1} - \frac{1}{x - 2}

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

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

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

= 2 ln ∣ x + 1 ∣ - ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x + 1 ∣ - ln ∣ x - 2 ∣ + C

\frac{\partial}{\partial x} (x^{6} y^{5} - x^{5} y^{4})

\frac{d}{d x} (e^{x y z} sin (x y) cos (2 x z))

\int_{0}^{1} (3 + x x) d x

\int ln (x^{5}) d x

\frac{d}{d x} (ln (8 x^{2}))