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

Lösung

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

arcsin (x) + C

Schritte zur Lösung

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

Vereinfache

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

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

Wende Exponentenregel an:

\frac{1}{a ^{b}} = a^{- b}

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

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

Trigonometrische Substitution anwenden

= \int 1 d u

Integral einer Konstanten :

\int a d x = a x

= 1 \cdot u

Setze in

u = arcsin (x)

ein

= 1 \cdot arcsin (x)

Vereinfache

= arcsin (x)

Füge eine Konstante zur Lösung hinzu

= arcsin (x) + C

\frac{\partial}{\partial s} (\frac{s - r}{t})

\frac{d}{d x} (\frac{x}{2 - x})

s l o p e x^{2} + y^{2} = 25

\int \frac{8}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

x^{2} \frac{d y}{d x} + 2 x y = 5 y^{4}