integral of (x+10)/(x^2-x-2)

Lösung

\int \frac{x + 10}{x ^{2} - x - 2} d x

- 3 ln ∣ x + 1 ∣ + 4 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{x + 10}{x ^{2} - x - 2} d x

Ermittle den Partialbruch von

\frac{x + 10}{x ^{2} - x - 2} : - \frac{3}{x + 1} + \frac{4}{x - 2}

= \int - \frac{3}{x + 1} + \frac{4}{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{3}{x + 1} d x + \int \frac{4}{x - 2} d x

\int \frac{3}{x + 1} d x = 3 ln ∣ x + 1 ∣

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

= - 3 ln ∣ x + 1 ∣ + 4 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= - 3 ln ∣ x + 1 ∣ + 4 ln ∣ x - 2 ∣ + C

\int_{- 3}^{0} (9 - x^{2}) d x

\frac{\partial}{\partial x} (7 y^{6} x^{6} - 6 y^{5} x^{5})

in v erse l a pl a ce \frac{4}{( s ^{2} + 4 )}

x \to \infty lim (csc (x))

3 \frac{d y}{d x} = x^{2}