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Solving a nasty rational differential equation

I have this nasty differential equation: ( Lorentz invariant elliptical 
invariant Klein-Gordon)
The substition I'm working with is the Kerr mass one of:
and J as an elliptical invariant like:
I isolate the radial part of the second differential ( in a polar four 
sopace the angular part isn't importyant mostly to mass radial solutions)
The Phi part is straight forfowd so I'm left with a double interagation
of a nasty rational function: ( m^2->r^4)
or  if
g[x_]=(-x20+228*x15-494*x10-228*x5-1)3/(1728*x^7 *(x10+11*x5-1)5)
What I tried after the Integration wouldn't stop in my Mathematica
was doing a term wise integration ( 64 terms, every 5th one non-zero).

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