# Integration is back

Calculus Level 5

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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