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

Lösung

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

Lösung

\frac{1}{2} (- arctan (x) + x) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

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

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

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

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (- arctan (x) + x) + C

Graph

Beliebte Beispiele

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

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

integral of 1/(sqrt(8x+2x^2))

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

limit as x approaches 2 of 2x^2+a/2 x-4

x \to 2 lim (2 x^{2} + \frac{a}{2} x - 4)

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

d er i v a t i v e (x^{2} - x + 2)^{3}

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

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