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Beliebt Rechnen >

integral of (sqrt(x^2+5))/(x^2)

Lösung

\int \frac{x ^{2} + 5}{x ^{2}} d x

Lösung

- \frac{x ^{2} + 5}{x} + ln \frac{1}{5} x + \frac{1}{5} (5 + x^{2}) + C

Schritte zur Lösung

\int \frac{x ^{2} + 5}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{x ^{2} + 5}{x} - \int - \frac{1}{x ^{2} + 5} d x

\int - \frac{1}{x ^{2} + 5} d x = - ln \frac{1}{5} x + \frac{1}{5} (5 + x^{2})

= - \frac{x ^{2} + 5}{x} - (- ln \frac{1}{5} x + \frac{1}{5} (5 + x^{2}))

Vereinfache

- \frac{x ^{2} + 5}{x} - (- ln \frac{1}{5} x + \frac{1}{5} (5 + x^{2})) : - \frac{x ^{2} + 5}{x} + ln \frac{1}{5} x + \frac{1}{5} (5 + x^{2})

= - \frac{x ^{2} + 5}{x} + ln \frac{1}{5} x + \frac{1}{5} (5 + x^{2})

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{2} + 5}{x} + ln \frac{1}{5} x + \frac{1}{5} (5 + x^{2}) + C

Graph

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