Complex Integral

Calculus Level 5

0cos(6x2)sin(6x2)1+x4dx\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 AπeBCD \dfrac { A\pi { e }^{ -B } }{ C\sqrt { D } } , where AA and CC are positive coprime integers, BB is an integer and DD is a square-free integer.

Find A+B+C+DA+B+C+D.

For more calculus problems see this.

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