\begin{equation*}
\int_{-\infty}^{\infty} \frac{\sin\pi x}{\Gamma\!(\pi-x) \Gamma\!(\pi+x)}\, \frac{\mathrm{d}x}{x}= \frac{\pi}{\Gamma\!(\pi)^2}
\end{equation*}
\begin{equation*}
\int_{-\infty}^{\infty} \frac{\sin\pi x}{\Gamma\!(\pi-x) \Gamma\!(\pi+x)}\, \frac{\mathrm{d}x}{x}= \frac{\pi}{\Gamma\!(\pi)^2}
\end{equation*}
Sir, it was such a beautiful integral because of the pi and gamma function.