Calculer les intégrales suivantes :
  1. $I_1 = \int_0^{\ln 3} \frac{e^x - e^{-x}}{e^x + e^{-x}} \,dx$ ; $I_2 = \int_2^3 (2-x)e^{x^2-4x} \,dx$
  2. $I_3 = \int_1^e \frac{dx}{x(1+\ln x)}$ ; $I_4 = \int_0^{\frac{pi}{3}} \frac{dx}{(3\tan x + 2)\cos^2 x}$
  3. $I_5 = \int_{\frac{pi}{6}}^{\frac{pi}{3}} \frac{\tan x}{\ln(\cos x)} \,dx$ ; $I_6 = \int_{\frac{pi}{6}}^{\frac{pi}{3}} \frac{\tan x}{\ln^3(\cos x)} \,dx$
  4. $I_7 = \int_1^3 \left(e^x \ln x + \frac{e^x}{x}\right) \,dx$ ; $I_8 = \int_0^1 \frac{(\arctan x)^2}{x^2+1} \,dx$
  5. $I_9 = \int_0^{\pi} e^x (\sin x + \cos x) \,dx$ ; $I_{10} = \int_0^{\frac{pi}{4}} \frac{e^{\tan x}}{\cos^2 x} \,dx$