\[\displaystyle\int _{ 0 }^{ \infty }{ \frac { \sin { \sqrt { x } } }{ { e }^{ x } } dx } =\frac { \sqrt [ A ]{ \pi } }{ B\sqrt [ C ]{ e } } \]

where \(A,B,C\)are positive integers then find

\(A+B+C\)

this is a part of Who's up to the challenge?

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