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#### karush

##### Well-known member

- Jan 31, 2012

- 2,749

\int {\frac{\sqrt{x^2-9}}{x}}\ dx

$

using

$\displaystyle

x=3\sec{\theta}\ \ \ dx=3\sin{\theta}\sec^2{\theta}\ d\theta

$

so then

$\displaystyle

\int {\frac{3\tan{\theta}}{3\sec{\theta}}}\ 3\sin{\theta}\sec^2{\theta}\ d\theta

\Rightarrow 3\int {\tan^2{\theta}}\ d\theta

$

the answer to this is

$\displaystyle

\sqrt{x^2-9}-3\sec^{-1}\left(x/3\right)+C

$

but after trying about 5 times can't seem to arrive at it..