# 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.

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