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Beliebt Rechnen >

integral of (sqrt(2-x^2))/x

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

= 2 - x^{2} - \int - \frac{2}{x - x ^{2} + 2} d x

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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