Complex Integral

Calculus Level 5

\[\large \displaystyle \int _{ 0 }^{ \infty }{ \dfrac { \cos\left( 6{ x }^{ 2 } \right) -\sin\left( 6{ x }^{ 2 } \right) }{ 1+{ x }^{ 4 } } \, dx } \]

The integral above is equal to \( \dfrac { A\pi { e }^{ -B } }{ C\sqrt { D } } \), where \(A\) and \(C\) are positive coprime integers, \(B\) is an integer and \(D\) is a square-free integer.