de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

x - \frac{3}{2} ln \frac{x}{2} + 1 + \frac{3}{2} ln \frac{x}{2} - 1 + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{2} + 2}{x ^{2} - 4} : \frac{x ^{2}}{x ^{2} - 4} + \frac{2}{x ^{2} - 4}

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

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

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

= - ln \frac{x}{2} + 1 + ln \frac{x}{2} - 1 + x - \frac{1}{2} ln \frac{x}{2} + 1 + \frac{1}{2} ln \frac{x}{2} - 1

Vereinfache

- ln \frac{x}{2} + 1 + ln \frac{x}{2} - 1 + x - \frac{1}{2} ln \frac{x}{2} + 1 + \frac{1}{2} ln \frac{x}{2} - 1 : x - \frac{3}{2} ln \frac{x}{2} + 1 + \frac{3}{2} ln \frac{x}{2} - 1

= x - \frac{3}{2} ln \frac{x}{2} + 1 + \frac{3}{2} ln \frac{x}{2} - 1

Füge eine Konstante zur Lösung hinzu

= x - \frac{3}{2} ln \frac{x}{2} + 1 + \frac{3}{2} ln \frac{x}{2} - 1 + C

Graph

Beliebte Beispiele

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

\int \frac{1}{x} \frac{1 + x}{x} d x

integral of (x+1)/(x^2-5x+6)

\int \frac{x + 1}{x ^{2} - 5 x + 6} d x

integral of (3/(1+x^2)-2/(sqrt(1-x^2)))

\int (\frac{3}{1 + x ^{2}} - \frac{2}{1 - x ^{2}}) d x

integral of (x+3)/(x^2-5x+6)

\int \frac{x + 3}{x ^{2} - 5 x + 6} d x

integral of cos(2x)sin(5x)

\int cos (2 x) sin (5 x) d x