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.

Find $A+B+C+D$ .

For more calculus problems see this.