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Beliebt Rechnen >

integral of (sqrt(x^2+9))/(x^3)

Lösung

\int \frac{x ^{2} + 9}{x ^{3}} d x

Lösung

- \frac{x ^{2} + 9}{2 x ^{2}} + \frac{1}{6} ln tan (\frac{1}{2} arctan (\frac{1}{3} x)) + C

Schritte zur Lösung

\int \frac{x ^{2} + 9}{x ^{3}} d x

Wende die partielle Integration an

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

\int - \frac{1}{2 x x ^{2} + 9} d x = - \frac{1}{6} ln tan (\frac{1}{2} arctan (\frac{1}{3} x))

= - \frac{x ^{2} + 9}{2 x ^{2}} - (- \frac{1}{6} ln tan (\frac{1}{2} arctan (\frac{1}{3} x)))

Vereinfache

= - \frac{x ^{2} + 9}{2 x ^{2}} + \frac{1}{6} ln tan (\frac{1}{2} arctan (\frac{1}{3} x))

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{2} + 9}{2 x ^{2}} + \frac{1}{6} ln tan (\frac{1}{2} arctan (\frac{1}{3} x)) + C

Graph

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