integral of (sqrt(x^2+64))/(x^2)

Lösung

\int \frac{x ^{2} + 64}{x ^{2}} d x

- \frac{x ^{2} + 64}{x} + ln (\frac{1}{8} x + 64 + x^{2}) + C

Schritte zur Lösung

\int \frac{x ^{2} + 64}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{x ^{2} + 64}{x} - \int - \frac{1}{x ^{2} + 64} d x

\int - \frac{1}{x ^{2} + 64} d x = - ln (\frac{1}{8} x + 64 + x^{2})

= - \frac{x ^{2} + 64}{x} - (- ln (\frac{1}{8} x + 64 + x^{2}))

Vereinfache

= - \frac{x ^{2} + 64}{x} + ln (\frac{1}{8} x + 64 + x^{2})

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{2} + 64}{x} + ln (\frac{1}{8} x + 64 + x^{2}) + C

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