integral of (x+2)/(x-4)

Lösung

\int \frac{x + 2}{x - 4} d x

6 ln ∣ x - 4 ∣ + x + C

Schritte zur Lösung

\int \frac{x + 2}{x - 4} d x

\frac{x + 2}{x - 4} = \frac{6}{x - 4} + 1

= \int \frac{6}{x - 4} + 1 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{6}{x - 4} d x + \int 1 d x

\int \frac{6}{x - 4} d x = 6 ln ∣ x - 4 ∣

\int 1 d x = x

= 6 ln ∣ x - 4 ∣ + x

Füge eine Konstante zur Lösung hinzu

= 6 ln ∣ x - 4 ∣ + x + C

(\frac{ln ^{2} ( x )}{x})^{^{'}}

x \to 2 lim (cos (x - 2))

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

\frac{d}{d x} (2 e^{- x^{2}} x)

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