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Beliebt Rechnen >

integral of (sqrt(4x^2-25))/(x^3)

Lösung

\int \frac{4 x ^{2} - 25}{x ^{3}} d x

Lösung

- \frac{4 x ^{2} - 25}{2 x ^{2}} + \frac{2}{5} arcsec (\frac{2}{5} x) + C

Schritte zur Lösung

\int \frac{4 x ^{2} - 25}{x ^{3}} d x

Wende die partielle Integration an

= - \frac{4 x ^{2} - 25}{2 x ^{2}} - \int - \frac{2}{x 4 x ^{2} - 25} d x

\int - \frac{2}{x 4 x ^{2} - 25} d x = - \frac{2}{5} arcsec (\frac{2}{5} x)

= - \frac{4 x ^{2} - 25}{2 x ^{2}} - (- \frac{2}{5} arcsec (\frac{2}{5} x))

Vereinfache

= - \frac{4 x ^{2} - 25}{2 x ^{2}} + \frac{2}{5} arcsec (\frac{2}{5} x)

Füge eine Konstante zur Lösung hinzu

= - \frac{4 x ^{2} - 25}{2 x ^{2}} + \frac{2}{5} arcsec (\frac{2}{5} x) + C

Graph

Beliebte Beispiele

derivative of 3e^x+(x-2^2)

\frac{d}{d x} (3 e^{x} + (x - 2)^{2})

limit as x approaches 6 of sqrt(5)

x \to 6 lim (5)

y^{''}+10y^'+25y=7e^{2x}

y^{^{''}} + 10 y^{^{'}} + 25 y = 7 e^{2 x}

integral from-infinity to 3 of xe^x

\int_{- \infty}^{3} x e^{x} d x

tangent 5e^xcos(x)(0.5)

t an g e n t 5 e^{x} cos (x) (0.5)