Find \(\displaystyle \int _{ 0 }^{ \infty }{ \frac { \cos { \left( tx \right) } }{ { x }^{ 2 }+1 } \,dx } \) at \(t=\ln { \left( \dfrac { \pi }{ 8 } \right) } \).

If this integral can be expressed as \( A\times \pi^B \) for rationals \(A\) and \(B\), find \(A\times B\).

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