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Beliebt Rechnen >

integral of 1/((x^2-1)^{1/2)}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{x}{( x ^{2} - 1 ) ^{\frac{1}{2}}} - \int - \frac{x ^{2}}{( x ^{2} - 1 ) ^{\frac{3}{2}}} d x

\int - \frac{x ^{2}}{( x ^{2} - 1 ) ^{\frac{3}{2}}} d x = \frac{x}{( x ^{2} - 1 ) ^{\frac{1}{2}}} - ln (x^{2} - 1)^{\frac{1}{2}} + x

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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