de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 7/(x(x^2+1))

Lösung

\int \frac{7}{x ( x ^{2} + 1 )} d x

Lösung

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

Schritte zur Lösung

\int \frac{7}{x ( x ^{2} + 1 )} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \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}

= 7 \cdot \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

= 7 (\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

= 7 (ln ∣ x ∣ - \frac{1}{2} ln x^{2} + 1)

Füge eine Konstante zur Lösung hinzu

= 7 (ln ∣ x ∣ - \frac{1}{2} ln x^{2} + 1) + C

Graph

Beliebte Beispiele

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

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

steigung (-3.1)(5.1)

s l o p e (- 3.1) (5.1)

(d^2)/(dx^2)((x^2)/(9+4x))

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{9 + 4 x})

f (θ) = θ

derivative of e^xx-e^x

\frac{d}{d x} (e^{x} x - e^{x})