Let $\:u_n(x):= \text{sin}(nx)e^{-nx}\:$
Let's also let$$\:\:w_n(y):=\int_{\pi}^{y} u_n(x)\text{d}x$$
Show that the series $$\sum_{n\in\mathbf{N}}w_n(y)$$
converges uniformly for$\:\:y\geq \pi$
I'm quite sure I need to use properties of complex analysis, of wich I'm not too savvy, but I need a head start on that one please =) so that any help'd be appriciated.
Thanks