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

Lösung

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

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

Schritte zur Lösung

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

\frac{- 1}{2} = - \frac{1}{2}

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

Wende die partielle Integration an

= \frac{x}{( 1 - x ) ^{\frac{1}{2}}} - \int \frac{x}{2 ( 1 - x ) ^{\frac{3}{2}}} d x

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

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

Füge eine Konstante zur Lösung hinzu

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

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