Who's up to the challenge? 8

Calculus Level 5

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

where A,B,CA,B,Care positive integers then find

A+B+CA+B+C


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

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