Definite integral

Calculus Level 5

If

\[\displaystyle\int _{ -\frac { 1 }{ \sqrt { 3 } } }^{ \frac { 1 }{ \sqrt { 3 } } }{ \frac { { x }^{ 4 } }{ 1-{ x }^{ 4 } } } \cos ^{ -1 } \left({ \frac { 2x }{ 1+{ x }^{ 2 } } } \right) dx \] can be represented in the form \[ \frac { \pi }{ a } [\pi +b\log { (c+\sqrt { 3 }) } +d\sqrt { 3 } ]\] then find the value of \(a+b+c+d\).

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