Expand it if you're crazy

Calculus Level 5

\(\displaystyle\int _{ 0 }^{ \infty }{ \frac { dx }{ ({ x }^{ 4 }+1)^{ 10 } } } =\frac { \pi }{ A!{ 2 }^{ B/C } } \displaystyle\prod _{ n=1 }^{ D }{ (Fn-G) }\\ \\ \)

where \(A,B,C,D,F,G\) are positive integers,then find \(A+B+C+D+F+G\)

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