integral of (2x)/((x+2)(x+1))

Lösung

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

2 (2 ln ∣ x + 2 ∣ - ln ∣ x + 1 ∣) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{x}{( x + 2 ) ( x + 1 )} d x

Ermittle den Partialbruch von

\frac{x}{( x + 2 ) ( x + 1 )} : \frac{2}{x + 2} - \frac{1}{x + 1}

= 2 \cdot \int \frac{2}{x + 2} - \frac{1}{x + 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

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

\int \frac{2}{x + 2} d x = 2 ln ∣ x + 2 ∣

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

= 2 (2 ln ∣ x + 2 ∣ - ln ∣ x + 1 ∣)

Füge eine Konstante zur Lösung hinzu

= 2 (2 ln ∣ x + 2 ∣ - ln ∣ x + 1 ∣) + C

\frac{\partial}{\partial x} (4 x - 2 y)

t an g e n t y = 4^{x}, (1, 4)

d er i v a t i v e (\frac{x ^{2} + 1}{x ^{2} - 1})^{3}

x \to 0 lim (2 x^{2})

\frac{d y}{d y}