I was doing some practice excersises for some diff eqs and this integral came up...now I got it right, but it was messy, can someone here give a better solution

$\displaystyle \int\sqrt{\frac{1}{x^2}+\frac{1}{x^4}}dx$

Now since the domain is every x greater than zero I rewrote this as

$\displaystyle \int\frac{\sqrt{1+x^2}}{x^2}dx$

Then said, Let $\displaystyle x=\tan(\theta)$

which is not fun, not hard, but not fun.

Is there a cool not obvious (or obvious) trick for this integral?