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^2+8-6x)

Lösung

\int \frac{1}{x ^{2} + 8 - 6 x} d x

Lösung

- \frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{1}{x ^{2} + 8 - 6 x} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} + 8 - 6 x} : - \frac{1}{2 ( x - 2 )} + \frac{1}{2 ( x - 4 )}

= \int - \frac{1}{2 ( x - 2 )} + \frac{1}{2 ( x - 4 )} 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}{2 ( x - 2 )} d x + \int \frac{1}{2 ( x - 4 )} d x

\int \frac{1}{2 ( x - 2 )} d x = \frac{1}{2} ln ∣ x - 2 ∣

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

= - \frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x - 4 ∣ + C

Graph

Beliebte Beispiele

integral of 1/(sqrt(3-4t^2))

\int \frac{1}{3 - 4 t ^{2}} d t

integral of 10^{-8}

\int 1 0^{- 8} d x

integral of (x^3+2x^2-5x+2)/(x^2+3x+2)

\int \frac{x ^{3} + 2 x ^{2} - 5 x + 2}{x ^{2} + 3 x + 2} d x

integral of 9xsqrt(3x^2-7)

\int 9 x 3 x^{2} - 7 d x

integral of (3x+1)/(sqrt(x))

\int \frac{3 x + 1}{x} d x