Calculer les intégrales suivantes :
  1. $C_1 = \int_{0}^{\pi} \left(\cos\frac{x}{2} - \sin 3x\right) \,dx$
  2. $C_2 = \int_{0}^{\pi} \sin^3(2x) \,dx$
  3. $C_3 = \int_{0}^{\pi} \sin^3 x \cos x \,dx$
  4. $C_4 = \int_{0}^{\frac{pi}{2}} \frac{\cos x}{2+\sin x} \,dx$
  5. $C_5 = \int_{\frac{pi}{3}}^{\frac{pi}{4}} \cos(2x)\sin(3x) \,dx$
  6. $C_6 = \int_{0}^{\frac{pi}{8}} \tan(2x) \,dx$
  7. $C_7 = \int_{0}^{\frac{pi}{4}} (\tan^3 x + \tan x) \,dx$
  8. $C_8 = \int_{\frac{pi}{4}}^{\pi^2} \frac{\cos\sqrt{x}}{\sqrt{x}} \,dx$
  9. $C_9 = \int_{0}^{\frac{pi}{4}} \tan^3 x \,dx$
  10. $C_{10} = \int_{0}^{\frac{pi}{3}} \frac{\cos(2x)}{(2+\sin 2x)^4} \,dx$