\[\large \int_{y=0}^a \int _{x=0}^{a-\sqrt { b-y^2}} \frac { xy\ln ( x+1729 )}{ ( x-a )^2} dx \ dy\]

If the integral above, where \(a=1729\) and \(b=2989441\), has a closed form of \(\dfrac c8 \left( 1+\ln { d } \right) \), find \(a+b+c+d\). (Note that \(a\), \(b\), \(c\) and \(d\) are not necessary distinct.)

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