Answer
$sec^{-1} |x|+C$
Work Step by Step
Consider $x=a \sec \theta$
Now, the given integral can be written as:
$\int\dfrac{\sec \theta \tan \theta}{\sec \theta \sqrt{\sec^2 \theta -1}} d\theta= \int \dfrac{\tan \theta}{\sqrt{\tan^2 \theta}}$
or, $= \int d \theta$
or, $=sec^{-1} |x|+C$
