Найти значение выражения:[latex]80( \sqrt{3} +1) \int\limits^ \frac{ \pi }{10} _ \frac{ \pi }{20} {sin(10x+ \frac{ \pi }{3} )} \, dx [/latex]

[latex]80(\sqrt{3}+1) \int\limits^\frac{\pi}{10}_{\frac{\pi}{20}} sin(10x+\frac{\pi}{3})dx=\\\\ 80(\sqrt{3}+1)*-\frac{1}{10}cos(10x+\frac{\pi}{3})|^{\frac{\pi}{10}}_{\frac{\pi}{20}}=\\\\ 80(\sqrt{3}+1) * -\frac{1}{10}*(cos(\pi+\frac{\pi}{3})-cos(\frac{\pi}{2}+\frac{\pi}{3}))=\\\\ -8(\sqrt{3}+1)(cos\frac{4\pi}{3}-cos\frac{5\pi}{6})=-8(\sqrt{3}+1)(\frac{1-\sqrt{3}}{2})=8[/latex]