Integral of $\log(1+x^{-2})$

Question

How can I find the integral of this function: $f(x) =\int{\log(1+\frac{1}{x^2})}dx$
What technique should I use?

Answer 1

$\int \log \frac{x^2+1}{x^2} dx= \int \log (x^2+1)dx -2\int \log x dx$

Both intrgrals can be found by integration by parts.