\int^{\infty}_{0}cosu(x-\xi)du=\lim_{\beta\rightarrow\infty }\int^{T}_{0}cosu(x-\xi)du=\lim_{\beta\rightarrow\infty }\frac{sinu(x-\xi)}{x-\xi}|^{\beta}_{0}=\lim_{\beta\rightarrow\infty}\frac{sin\beta(x-\xi)}{x-\xi} }