de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (7x^2+5x-6)/((x^2-4)(x+2))

Lösung

\int \frac{7 x ^{2} + 5 x - 6}{( x ^{2} - 4 ) ( x + 2 )} d x

Lösung

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

Schritte zur Lösung

\int \frac{7 x ^{2} + 5 x - 6}{( x ^{2} - 4 ) ( x + 2 )} d x

Ermittle den Partialbruch von

\frac{7 x ^{2} + 5 x - 6}{( x ^{2} - 4 ) ( x + 2 )} : \frac{5}{x + 2} - \frac{3}{( x + 2 ) ^{2}} + \frac{2}{x - 2}

= \int \frac{5}{x + 2} - \frac{3}{( x + 2 ) ^{2}} + \frac{2}{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{5}{x + 2} d x - \int \frac{3}{( x + 2 ) ^{2}} d x + \int \frac{2}{x - 2} d x

\int \frac{5}{x + 2} d x = 5 ln ∣ x + 2 ∣

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

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

= 5 ln ∣ x + 2 ∣ - (- \frac{3}{x + 2}) + 2 ln ∣ x - 2 ∣

Vereinfache

= 5 ln ∣ x + 2 ∣ + \frac{3}{x + 2} + 2 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= 5 ln ∣ x + 2 ∣ + \frac{3}{x + 2} + 2 ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

f (x) = x^{4 x}

limit as x approaches 1 of-6xsin(3x^2+1)

x \to 1 lim (- 6 x sin (3 x^{2} + 1))

derivative f(x)=(4x)/(x+2)

d er i v a t i v e f (x) = \frac{4 x}{x + 2}

(\partial)/(\partial x)(2x^2e^{xy^2})

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

derivative y=log_{2}(5x)

d er i v a t i v e y = lo g_{2} (5 x)