Răspuns:
[tex]\int a^x dx = \frac{a^x}{ln a} +\mathcal C[/tex].
[tex]\int_0^1 (2002^x+2002^{-x})dx = \int_0^1 2002^x dx + \int_0^1 (\frac{1}{2002})^x dx = \frac{2002^x}{ln(2002)}|_0^1 + \frac{2002^{-x}}{-ln(2002)}|_0^1 =[/tex]
[tex]=\frac{2002-1}{ln(2002)}+\frac{2002^{-1}-1}{-ln(2002)}=\frac{2002-2002^{-1}}{ln(2002)}.[/tex]
Am folosit faptul ca: [tex]2002^{-1}=\frac{1}{2002},ln(2002^{-1})=-ln(2002).[/tex]
