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/(sqrt(1-x^2)))

Lösung

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

Lösung

- 1 - x^{2} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int - \frac{1}{2 u} d u

Entferne die Konstante:

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

= - \frac{1}{2} \cdot \int \frac{1}{u} d u

Wende die Potenzregel an

= - \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Setze in

u = 1 - x^{2}

ein

= - \frac{1}{2} \cdot 2 (1 - x^{2})^{\frac{1}{2}}

Vereinfache

- \frac{1}{2} \cdot 2 (1 - x^{2})^{\frac{1}{2}} : - 1 - x^{2}

= - 1 - x^{2}

Füge eine Konstante zur Lösung hinzu

= - 1 - x^{2} + C

Graph

Beliebte Beispiele

integral from-4 to 0 of |x+2|

\int_{- 4}^{0} ∣ x + 2 ∣ d x

(\partial)/(\partial x)(4-x^2-2y^2)

\frac{\partial}{\partial x} (4 - x^{2} - 2 y^{2})

derivative of Ax^2e^{3x}

\frac{d}{d x} (A x^{2} e^{3 x})

x(dy)/(dx)=3xe^x-y+6x^2

x \frac{d y}{d x} = 3 x e^{x} - y + 6 x^{2}

limit as x approaches 1 of x^{4/(1-x)}

x \to 1 lim (x^{\frac{4}{1 - x}})