Обчисліть інтеграл ∫

Решите задачу:

$\large\int_{0}^{\pi}\cos^2{\left (x\over3 \right )}\: \mathrm{dx}=***\\ \cos^2{\left (x\over3 \right )}={1\over2}\left (1+\cos{\left ( 2x\over3 \right )} \right )\\ ***={1\over2}\int_{0}^{\pi}\left (1+\cos{\left ( 2x\over3 \right )} \right )\: \mathrm{dx}={x\over2}|_{0}^{\pi}+{1\over2}\cdot{3\over2}\int_{0}^{\pi}\cos{\left ( 2x\over3 \right )}\: \mathrm{d{2x\over3}}={\pi\over2}+{3\over4}\sin{\left ( 2x\over3 \right )}|_{0}^{\pi}={\pi\over2}+{3\over4}\sin{\left ( 2\pi\over3 \right )}={\pi\over2}+{3\over4}\cdot{\sqrt{3}\over2}={\pi\over2}+{3\sqrt{3}\over8}$