Calculer les intégrales suivantes :
  1. $D_1 = \int_1^2 \frac{1}{x^2}e^{\frac{1}{x}} \,dx$ ; $D_2 = \int_0^{\frac{pi}{2}} \sin(2x)e^{\cos^2 x} \,dx$
  2. $D_3 = \int_1^{e^2} \frac{\ln t}{t} \,dt$ ; $D_4 = \int_0^1 (2^x + 3^x) \,dx$
  3. $D_5 = \int_1^e \left(x+\frac{1}{x}\right)(1+\ln x) \,dx$ ; $D_6 = \int_e^{e^4} \frac{dt}{t \ln t}$
  4. $D_7 = \int_1^{e^{\pi}} \frac{\cos(\ln x)}{x} \,dx$ ; $D_8 = \int_0^3 \frac{\ln(1+\sqrt{x})}{x+\sqrt{x}} \,dx$
  5. $D_9 = \int_e^{e^2} \frac{dt}{t \ln^2 t}$ ; $D_{10} = \int_{\ln 2}^{\ln 3} \frac{(e^x+1)(e^x+2)}{e^x} \,dx$