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

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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