Calculer les intégrales suivantes :
  1. $I_1 = \int_0^{\frac{\pi}{4}} \frac{\cos x}{1+\cos x} \,dx\qquad $ ; $\qquad I_2 = \int_0^{\frac{\pi}{3}} \sin(2x)\cos(5x) \,dx$
  2. $I_3 = \int_0^{\ln(\sqrt{3})} e^x \text{Arctan}(e^{-x}) \,dx\qquad $ ; $\qquad I_4 = \int_0^{\frac{\pi}{3}} \sin^4(x) \,dx$
  3. $I_5 = \int_0^{\frac{\pi}{2}} (2x+1)\cos^2(x)\sin(x) \,dx\qquad $ ; $\qquad I_6 = \int_0^1 x^3 e^{-x^2} \,dx$
  4. $I_7 = \int_{\frac{pi}{2}}^{\pi} (x\cos x + \sin x) \,dx \qquad $ ; $\qquad I_8 = \int_{\frac{\pi}{3}}^{\frac{\pi}{4}} \tan(x) \,dx$