I'm working on a Linear Coefficients problem of the form G(ax+by):

$\displaystyle (3x-2y-6)dx-(2y-3x+2)dy=0$

I've managed to reduce it to the following,

$\displaystyle \int dx\ = \int -dz\frac{2-z}{5z-18}\\$

where $\displaystyle z = 3x-2y$

But I don't know how to finish this. I've scanned the table integrals in my book to no avail and I'm not sure how I'd use u substitution. Please lead me down the right path.