$\displaystyle 2r(s^2+1)dr+(r^4+1)ds=0$

This is the second question in the textbook and I am able to do every question after it, so perhaps there is something simple that I am not seeing? The answer has no trig functions in it.

$\displaystyle (2r)/(r^4+1)dr+(s^2+1)ds=0$

The only way I can integrate the dr term is with trig functions, but according the the answers there is a simple way such that no trig functions are required.