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Beliebt Rechnen >

integral of (sqrt(9x^2-16))/(x^3)

Lösung

\int \frac{9 x ^{2} - 16}{x ^{3}} d x

Lösung

- \frac{9 x ^{2} - 16}{2 x ^{2}} + \frac{9}{8} arcsec (\frac{3}{4} x) + C

Schritte zur Lösung

\int \frac{9 x ^{2} - 16}{x ^{3}} d x

Wende die partielle Integration an

= - \frac{9 x ^{2} - 16}{2 x ^{2}} - \int - \frac{9}{2 x 9 x ^{2} - 16} d x

\int - \frac{9}{2 x 9 x ^{2} - 16} d x = - \frac{9}{8} arcsec (\frac{3}{4} x)

= - \frac{9 x ^{2} - 16}{2 x ^{2}} - (- \frac{9}{8} arcsec (\frac{3}{4} x))

Vereinfache

= - \frac{9 x ^{2} - 16}{2 x ^{2}} + \frac{9}{8} arcsec (\frac{3}{4} x)

Füge eine Konstante zur Lösung hinzu

= - \frac{9 x ^{2} - 16}{2 x ^{2}} + \frac{9}{8} arcsec (\frac{3}{4} x) + C

Graph

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