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-3)/(x^2+3x+3)

Lösung

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

Lösung

\frac{1}{2} ln 4 x^{2} + 12 x + 12 - 33 arctan (\frac{2}{3} x + 3) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x - 3}{x ^{2} + 3 x + 3} : \frac{x}{x ^{2} + 3 x + 3} - \frac{3}{x ^{2} + 3 x + 3}

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

\int \frac{x}{x ^{2} + 3 x + 3} d x = \frac{1}{2} ln 4 x^{2} + 12 x + 12 - 3 arctan (\frac{2}{3} x + 3)

\int \frac{3}{x ^{2} + 3 x + 3} d x = 23 arctan (\frac{2}{3} x + 3)

= \frac{1}{2} ln 4 x^{2} + 12 x + 12 - 3 arctan (\frac{2}{3} x + 3) - 23 arctan (\frac{2}{3} x + 3)

Vereinfache

= \frac{1}{2} ln 4 x^{2} + 12 x + 12 - 33 arctan (\frac{2}{3} x + 3)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln 4 x^{2} + 12 x + 12 - 33 arctan (\frac{2}{3} x + 3) + C

Graph

Beliebte Beispiele

integral of ((sqrt(x)-x)/(x^2))

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

integral of 10(y^4-y+1)

\int 10 (y^{4} - y + 1) d y

integral of (2e^xtan^2(e^x))/(sin(e^x))

\int \frac{2 e ^{x} tan ^{2} ( e ^{x} )}{sin ( e ^{x} )} d x

integral of e^{jwt}

\int e^{j wt} d t

integral of sqrt(2+4t^2)

\int 2 + 4 t^{2} d t