integral of (-341x+342)/(x^2+x-2)

Lösung

\int \frac{- 341 x + 342}{x ^{2} + x - 2} d x

\frac{1}{3} ln ∣ x - 1 ∣ - \frac{1024}{3} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{- 341 x + 342}{x ^{2} + x - 2} d x

Ermittle den Partialbruch von

\frac{- 341 x + 342}{x ^{2} + x - 2} : \frac{1}{3 ( x - 1 )} - \frac{1024}{3 ( x + 2 )}

= \int \frac{1}{3 ( x - 1 )} - \frac{1024}{3 ( 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{1}{3 ( x - 1 )} d x - \int \frac{1024}{3 ( x + 2 )} d x

\int \frac{1}{3 ( x - 1 )} d x = \frac{1}{3} ln ∣ x - 1 ∣

\int \frac{1024}{3 ( x + 2 )} d x = \frac{1024}{3} ln ∣ x + 2 ∣

= \frac{1}{3} ln ∣ x - 1 ∣ - \frac{1024}{3} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} ln ∣ x - 1 ∣ - \frac{1024}{3} ln ∣ x + 2 ∣ + C

\frac{\partial}{\partial x} (3 x sin (9 x^{2} y))

x \to \infty lim ((1 + x)^{\frac{3}{x}})

\int \frac{1}{x ^{2} + 36} d x

x \to - \infty lim (\frac{x ^{2} + 2}{x ^{3} + x ^{2} - 1})

x \to 0 lim (7 x^{3} + \frac{1}{4} x^{2})