# Does an elementary method exist?

Calculus Level 5

$\large{\displaystyle \int^{\infty}_{- \infty} \frac{\sin x}{x^2+4x+5}\, dx}$

If the value of the above integral is equal to $$- \pi^{A} e^{B} \sin C$$ where $$A,B$$ and $$C$$ are integers, find $$A \times B \times C$$.

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