Problem: $\displaystyle y*(1+x)+2xy'=0$

I have rearranged the equation to put it in exact form, resulting in the equation:

$\displaystyle (y+xy)dx+2xdy=0$

After that I found my $\displaystyle \frac{\partial M}{\partial y}$ and $\displaystyle \frac{\partial N}{\partial x}$

This leads to a complicated integrating factor of $\displaystyle e^{-\frac{1}{2}(ln|x|-x)}$

Am I on the correct track?