integral of (4x-11)/(2x^2+7x-4)

Lösung

\int \frac{4 x - 11}{2 x ^{2} + 7 x - 4} d x

- ln ∣ 2 x - 1 ∣ + 3 ln ∣ x + 4 ∣ + C

Schritte zur Lösung

\int \frac{4 x - 11}{2 x ^{2} + 7 x - 4} d x

Ermittle den Partialbruch von

\frac{4 x - 11}{2 x ^{2} + 7 x - 4} : - \frac{2}{2 x - 1} + \frac{3}{x + 4}

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

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

\int \frac{3}{x + 4} d x = 3 ln ∣ x + 4 ∣

= - ln ∣ 2 x - 1 ∣ + 3 ln ∣ x + 4 ∣

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (\frac{x ^{3} + x ^{2} - x + 2}{x + 2})

x \to 0 lim (\frac{( a ^{x} - 1 )}{x})

\int_{1}^{5} (x + 1)^{2} d x

d er i v a t i v e (t^{2} + 1) (t - \frac{1}{t})

\frac{\partial}{\partial x} (2 x^{y})