Inspired by Surya Prakash

Calculus Level 5

\[\large \displaystyle \int _{ 0 }^{ \infty }{ { e }^{ -\sqrt { 3 } { x }^{ \frac { 2 }{ 3 } } }\sin\left( { x }^{ \frac { 2 }{ 3 } } \right) \, dx }\]

Given that the integral above is equal to \(\dfrac {3\pi^A} B \) for rational numbers \(A\) and \(B\), find the value of \(A \times B\).

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