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

Lösung

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

Lösung

ln ∣ x ∣ - ln x^{2} + 1 + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

Addiere gleiche Elemente:

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

= ln ∣ x ∣ - ln x^{2} + 1

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - ln x^{2} + 1 + C

Graph

Beliebte Beispiele

integral of e^x+x^2

\int e^{x} + x^{2} d x

derivative of 3x^7

\frac{d}{d x} (3 x^{7})

derivative f(r)=sqrt(r)+\sqrt[7]{r}

d er i v a t i v e f (r) = r + 7 r

integral of (2xe^{-3x})

\int (2 x e^{- 3 x}) d x

y^'+2sin(2x)y=2sin(2x),y(pi/2)=3

y^{^{'}} + 2 sin (2 x) y = 2 sin (2 x), y (\frac{π}{2}) = 3