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Beliebt Rechnen >

integral of (sqrt(x^2-1))/(x^2)

Lösung

\int \frac{x ^{2} - 1}{x ^{2}} d x

Lösung

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

Schritte zur Lösung

\int \frac{x ^{2} - 1}{x ^{2}} d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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