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+6)/(x^2+4)

Lösung

\int \frac{x + 6}{x ^{2} + 4} d x

Lösung

\frac{1}{2} ln x^{2} + 4 + 3 arctan (\frac{x}{2}) + C

Schritte zur Lösung

\int \frac{x + 6}{x ^{2} + 4} d x

Multipliziere aus

\frac{x + 6}{x ^{2} + 4} : \frac{x}{x ^{2} + 4} + \frac{6}{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}{x ^{2} + 4} d x + \int \frac{6}{x ^{2} + 4} d x

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

\int \frac{6}{x ^{2} + 4} d x = 3 arctan (\frac{x}{2})

= \frac{1}{2} ln x^{2} + 4 + 3 arctan (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 4 + 3 arctan (\frac{x}{2}) + C

Graph

Beliebte Beispiele

integral of 8xcos(4x^2+3)

\int 8 x cos (4 x^{2} + 3) d x

limit as h approaches 0 of (cosh(x))/h

h \to 0 lim (\frac{cosh ( x )}{h})

x(dy)/(dx)=y(ln(y)-ln(x))

x \frac{d y}{d x} = y (ln (y) - ln (x))

derivative of (ln(x-1)/(ln^2(x)))

\frac{d}{d x} (\frac{ln ( x ) - 1}{ln ^{2} ( x )})

fläche (12)/(1+x^4),6x^2

a re a \frac{12}{1 + x ^{4}}, 6 x^{2}