integral of (3x-4)/(x^2-x-2)

Lösung

\int \frac{3 x - 4}{x ^{2} - x - 2} d x

\frac{7}{3} ln ∣ x + 1 ∣ + \frac{2}{3} ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{3 x - 4}{x ^{2} - x - 2} d x

Ermittle den Partialbruch von

\frac{3 x - 4}{x ^{2} - x - 2} : \frac{7}{3 ( x + 1 )} + \frac{2}{3 ( x - 2 )}

= \int \frac{7}{3 ( x + 1 )} + \frac{2}{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{7}{3 ( x + 1 )} d x + \int \frac{2}{3 ( x - 2 )} d x

\int \frac{7}{3 ( x + 1 )} d x = \frac{7}{3} ln ∣ x + 1 ∣

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

= \frac{7}{3} ln ∣ x + 1 ∣ + \frac{2}{3} ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{7}{3} ln ∣ x + 1 ∣ + \frac{2}{3} ln ∣ x - 2 ∣ + C

\int \frac{5 x ^{2} + 9 x + 5}{( x ^{2} + 1 ) ^{2}} d x

\frac{d}{d a} (sin (a) - sin (2 a) + sin (3 a))

x \to 0 - lim (x cot (x))

d er i v a t i v e y = \frac{7}{x ^{3}}

\frac{y ^{^{'}}}{y - y ^{2}} = \frac{t}{( 1 + t ^{2} )}