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Beliebt Rechnen >

integral of (sqrt(64x^2-25))/(x^3)

Lösung

\int \frac{64 x ^{2} - 25}{x ^{3}} d x

Lösung

- \frac{64 x ^{2} - 25}{2 x ^{2}} + \frac{32}{5} arcsec (\frac{8}{5} x) + C

Schritte zur Lösung

\int \frac{64 x ^{2} - 25}{x ^{3}} d x

Wende die partielle Integration an

= - \frac{64 x ^{2} - 25}{2 x ^{2}} - \int - \frac{32}{x 64 x ^{2} - 25} d x

\int - \frac{32}{x 64 x ^{2} - 25} d x = - \frac{32}{5} arcsec (\frac{8}{5} x)

= - \frac{64 x ^{2} - 25}{2 x ^{2}} - (- \frac{32}{5} arcsec (\frac{8}{5} x))

Vereinfache

= - \frac{64 x ^{2} - 25}{2 x ^{2}} + \frac{32}{5} arcsec (\frac{8}{5} x)

Füge eine Konstante zur Lösung hinzu

= - \frac{64 x ^{2} - 25}{2 x ^{2}} + \frac{32}{5} arcsec (\frac{8}{5} x) + C

Graph

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