I didn't expect that coming

Calculus Level 5

\[\large{\left[ \frac { { d }^{ 2 } }{ d{ x }^{ 2 } } \left( \sin ^{ -1 }{ \left( 2{ x }^{ 2 }+4 \right) } +\cos { \left( \frac { 2x }{ 7{ x }^{ 2 }+1 } \right) } \right) \right] _{ x=\sqrt { 2 } }}\]

If the value of above given second derivative can be expressed as

\[\large{\\ \frac { Ai }{ B\sqrt { C } } -\frac { D\sqrt { E } \sin { \left( \frac { E\sqrt { E } }{ F } \right) } }{ G } -\frac { H\cos { \left( \frac { E\sqrt { E } }{ F } \right) } }{ J } }\]

For integers \(A,B,C,D,E,F,G,H,J\) and \(E,C\) are square-free and \(i^{2}=-1\),

Find \(A+B+C+D+E+F+G+H+J\)

Note:-

\(\gcd{(A,B)}=\gcd{(D,F)}=\gcd{(E,F)}=\gcd{(H,J)}=1\)

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