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Beliebt Rechnen >

integral of ((9-x^2)^{1/2})/(x^2)

Lösung

\int \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x ^{2}} d x

Lösung

- \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x} - arcsin (\frac{1}{3} x) + C

Schritte zur Lösung

\int \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x} - \int \frac{1}{( 9 - x ^{2} ) ^{\frac{1}{2}}} d x

\int \frac{1}{( 9 - x ^{2} ) ^{\frac{1}{2}}} d x = arcsin (\frac{1}{3} x)

= - \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x} - arcsin (\frac{1}{3} x)

Füge eine Konstante zur Lösung hinzu

= - \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x} - arcsin (\frac{1}{3} x) + C

Graph

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