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

Lösung

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

\frac{x}{( x - 2 ) ^{\frac{1}{2}}} + \frac{x - 4}{( x - 2 ) ^{\frac{1}{2}}} + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - \frac{x}{2 ( x - 2 ) ^{\frac{3}{2}}} d x = - \frac{x - 4}{( x - 2 ) ^{\frac{1}{2}}}

= \frac{x}{( x - 2 ) ^{\frac{1}{2}}} - (- \frac{x - 4}{( x - 2 ) ^{\frac{1}{2}}})

Vereinfache

= \frac{x}{( x - 2 ) ^{\frac{1}{2}}} + \frac{x - 4}{( x - 2 ) ^{\frac{1}{2}}}

Füge eine Konstante zur Lösung hinzu

= \frac{x}{( x - 2 ) ^{\frac{1}{2}}} + \frac{x - 4}{( x - 2 ) ^{\frac{1}{2}}} + C

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