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Beliebt Rechnen >

integral of (sqrt(16+x^2))/(x^2)

Lösung

\int \frac{16 + x ^{2}}{x ^{2}} d x

Lösung

- \frac{16 + x ^{2}}{x} + ln (\frac{1}{4} x + 16 + x^{2}) + C

Schritte zur Lösung

\int \frac{16 + x ^{2}}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{16 + x ^{2}}{x} - \int - \frac{1}{16 + x ^{2}} d x

\int - \frac{1}{16 + x ^{2}} d x = - ln (\frac{1}{4} x + 16 + x^{2})

= - \frac{16 + x ^{2}}{x} - (- ln (\frac{1}{4} x + 16 + x^{2}))

Vereinfache

= - \frac{16 + x ^{2}}{x} + ln (\frac{1}{4} x + 16 + x^{2})

Füge eine Konstante zur Lösung hinzu

= - \frac{16 + x ^{2}}{x} + ln (\frac{1}{4} x + 16 + x^{2}) + C

Graph

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