de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (8x+12)/(x*(x^2+4))

Lösung

\int \frac{8 x + 12}{x \cdot ( x ^{2} + 4 )} d x

Lösung

4 arctan (\frac{x}{2}) + 12 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4) + C

Schritte zur Lösung

\int \frac{8 x + 12}{x ( x ^{2} + 4 )} d x

Multipliziere aus

\frac{8 x + 12}{x ( x ^{2} + 4 )} : \frac{8 x}{x ( x ^{2} + 4 )} + \frac{12}{x ( 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{8 x}{x ( x ^{2} + 4 )} d x + \int \frac{12}{x ( x ^{2} + 4 )} d x

\int \frac{8 x}{x ( x ^{2} + 4 )} d x = 4 arctan (\frac{x}{2})

\int \frac{12}{x ( x ^{2} + 4 )} d x = 12 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4)

= 4 arctan (\frac{x}{2}) + 12 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4)

Füge eine Konstante zur Lösung hinzu

= 4 arctan (\frac{x}{2}) + 12 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4) + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(xsqrt(1+y^3))

\frac{\partial}{\partial x} (x 1 + y^{3})

limit as x approaches 1 of (2-2/x)^2

x \to 1 lim ((2 - \frac{2}{x})^{2})

tangent 3x^2-1,\at x=-2

t an g e n t 3 x^{2} - 1, at x = - 2

tangent y=(x^2+2)/(x+8),(3,1)

t an g e n t y = \frac{x ^{2} + 2}{x + 8}, (3, 1)

integral of 2e^{3x-5}

\int 2 e^{3 x - 5} d x