$\int_{0}^{1}u^k\cot{\frac{\pi(1-u)}{m}}\sin{\frac{2\pi n(1-u)}{m}}\,du$
What is the limit of this integral as $n$ approaches infinity for integer $k\geq 0$ and real $m\geq 1$?
user130611
$\int_{0}^{1}u^k\cot{\frac{\pi(1-u)}{m}}\sin{\frac{2\pi n(1-u)}{m}}\,du$