de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

ln x^{2} + 4 + 2 arctan (\frac{x}{2}) + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{4}{x ^{2} + 4} d x = 2 arctan (\frac{x}{2})

= ln x^{2} + 4 + 2 arctan (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= ln x^{2} + 4 + 2 arctan (\frac{x}{2}) + C

Graph

Beliebte Beispiele

integral of (2x^2)/(1+sin(8)x^3)

\int \frac{2 x ^{2}}{1 + sin ( 8 ) x ^{3}} d x

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

\int \frac{2 x + 5}{x ^{2} + 5 x - 7} d x

integral of+sin^4(3t)cos^4(3t)

\int + sin^{4} (3 t) cos^{4} (3 t) d t

integral of x^2sqrt(9-4x^2)

\int x^{2} 9 - 4 x^{2} d x

integral of ((4x+3)/(2x+5))

\int (\frac{4 x + 3}{2 x + 5}) d x