de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 1/(x(x^2+1))

Lösung

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

Lösung

ln ∣ x ∣ - \frac{1}{2} ln x^{2} + 1 + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{x ( x ^{2} + 1 )} : \frac{1}{x} - \frac{x}{x ^{2} + 1}

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - \frac{1}{2} ln x^{2} + 1

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative cos(e^{-t^2})

d er i v a t i v e cos (e^{- t^{2}})

integral from 0 to pi of sin(6x)cos(3x)

\int_{0}^{π} sin (6 x) cos (3 x) d x

integral of-2e^x(e^x-1)^3

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

derivative 9arctan(x-sqrt(1+x^2))

d er i v a t i v e 9 arctan (x - 1 + x^{2})

steigung (19,-16),(-7,-15)

s l o p e (19, - 16), (- 7, - 15)