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

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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