integral of (4x-11)/(x^2-3x-4)

Lösung

\int \frac{4 x - 11}{x ^{2} - 3 x - 4} d x

3 ln ∣ x + 1 ∣ + ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{4 x - 11}{x ^{2} - 3 x - 4} d x

Ermittle den Partialbruch von

\frac{4 x - 11}{x ^{2} - 3 x - 4} : \frac{3}{x + 1} + \frac{1}{x - 4}

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

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

\int \frac{1}{x - 4} d x = ln ∣ x - 4 ∣

= 3 ln ∣ x + 1 ∣ + ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x + 1 ∣ + ln ∣ x - 4 ∣ + C

\frac{d}{d x} (e^{x} cos (3 x))

x \to 5 - lim (\frac{x - 6}{x - 5})

ma c l a u r in e^{- 5 x}

3 y^{^{'}} - 6 y = 12

t \frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} = t^{2}