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^2-x+28)/(x^3+7x)

Lösung

\int \frac{x ^{2} - x + 28}{x ^{3} + 7 x} d x

Lösung

4 ln ∣ x ∣ - \frac{3}{2} ln x^{2} + 7 - \frac{1}{7} arctan (\frac{x}{7}) + C

Schritte zur Lösung

\int \frac{x ^{2} - x + 28}{x ^{3} + 7 x} d x

Ermittle den Partialbruch von

\frac{x ^{2} - x + 28}{x ^{3} + 7 x} : \frac{4}{x} + \frac{- 3 x - 1}{x ^{2} + 7}

= \int \frac{4}{x} + \frac{- 3 x - 1}{x ^{2} + 7} 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{4}{x} d x + \int \frac{- 3 x - 1}{x ^{2} + 7} d x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int \frac{- 3 x - 1}{x ^{2} + 7} d x = - \frac{3}{2} ln x^{2} + 7 - \frac{1}{7} arctan (\frac{x}{7})

= 4 ln ∣ x ∣ - \frac{3}{2} ln x^{2} + 7 - \frac{1}{7} arctan (\frac{x}{7})

Füge eine Konstante zur Lösung hinzu

= 4 ln ∣ x ∣ - \frac{3}{2} ln x^{2} + 7 - \frac{1}{7} arctan (\frac{x}{7}) + C

Graph

Beliebte Beispiele

integral of (-2x^2+8x-20)/(x^2-4x+8)

\int \frac{- 2 x ^{2} + 8 x - 20}{x ^{2} - 4 x + 8} d x

sum from n=1 to infinity of 1/(1+3^n)

n = 1 \sum \infty \frac{1}{1 + 3 ^{n}}

x d y = 4 y d x

derivative sin(xy)+pi

d er i v a t i v e sin (x y) + π

(dy)/(dx)= x/(ysqrt(1+x))

\frac{d y}{d x} = \frac{x}{y 1 + x}