\(\rm \displaystyle\int \frac{e^{\log(1 + 1/x^2)}}{x^2 + \frac{1}{x^2}} dx\) is equal to
1
\(\rm \frac{1}{\sqrt 2} \tan^{-1} \left( x - \frac{1}{x} \right)\)
2
\(-\rm \frac{1}{\sqrt 2} \tan^{-1} \left( x - \frac{1}{x} \right)\)
3
\(\rm \frac{1}{\sqrt 2} \log \left( \frac{x^2 + 1}{x \sqrt 2} \right)\)
4
\(\rm \frac{1}{\sqrt 2} \tan^{-1} \left( \frac{x^2 - 1}{x \sqrt 2} \right)\)