How do you find the integral of $dx /( (x^2)*sqrt((x^2)-1))$ ?

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Answer 1 · 2015-09-09T07:50:19

$sqrt(1-1/x^2) + C$

Finding this integral is easy by susbstituting $x= sectheta$ so that $dx= sectheta tantheta d theta$

$int dx/(x^2* sqrt (x^2-1)$ = $int (sectheta tan theta d theta)/(sec^2 theta tan theta$

= $int costheta d theta$ = $sintheta +C$ = $sqrt(1-1/x^2) + C$

How do you find the integral of dx /( (x^2)*sqrt((x^2)-1))dx /( (x^2)*sqrt((x^2)-1))?