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

Lösung

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

Lösung

x - 3 arctan (x) + C

Schritte zur Lösung

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

Vereinfache

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

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

Multipliziere aus

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

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

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

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

= - arctan (x) + x - 2 arctan (x)

Vereinfache

= x - 3 arctan (x)

Füge eine Konstante zur Lösung hinzu

= x - 3 arctan (x) + C

Graph

Beliebte Beispiele

integral of (e^{arctan(x)}-2x)/(1+x^2)

\int \frac{e ^{a r c t a n (x)} - 2 x}{1 + x ^{2}} d x

integral of (x+4)e^{-2x}

\int (x + 4) e^{- 2 x} d x

integral of (16x^2)/(sqrt(49-x^2))

\int \frac{16 x ^{2}}{49 - x ^{2}} d x

integral of 1-1(2x+2)

\int 1 - 1 (2 x + 2) d x

integral of (x/(x^2+6x+8))^2

\int (\frac{x}{x ^{2} + 6 x + 8})^{2} d x