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Beliebt Rechnen >

integral of (sqrt(16x^2-9))/(x^4)

Lösung

\int \frac{16 x ^{2} - 9}{x ^{4}} d x

Lösung

- \frac{16 x ^{2} - 9}{3 x ^{3}} + \frac{16 16 x ^{2} - 9}{27 x} + C

Schritte zur Lösung

\int \frac{16 x ^{2} - 9}{x ^{4}} d x

Wende die partielle Integration an

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

\int - \frac{16}{3 x ^{2} 16 x ^{2} - 9} d x = - \frac{16 16 x ^{2} - 9}{27 x}

= - \frac{16 x ^{2} - 9}{3 x ^{3}} - (- \frac{16 16 x ^{2} - 9}{27 x})

Vereinfache

= - \frac{16 x ^{2} - 9}{3 x ^{3}} + \frac{16 16 x ^{2} - 9}{27 x}

Füge eine Konstante zur Lösung hinzu

= - \frac{16 x ^{2} - 9}{3 x ^{3}} + \frac{16 16 x ^{2} - 9}{27 x} + C

Graph

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