Question

Ce metoda se aplica in cazul urmatoarei integrale?

Answer 1

Răspuns:

$\int a^x dx = \frac{a^x}{ln a} +\mathcal C$.

$\int_0^1 (2002^x+2002^{-x})dx = \int_0^1 2002^x dx + \int_0^1 (\frac{1}{2002})^x dx = \frac{2002^x}{ln(2002)}|_0^1 + \frac{2002^{-x}}{-ln(2002)}|_0^1 =$

$=\frac{2002-1}{ln(2002)}+\frac{2002^{-1}-1}{-ln(2002)}=\frac{2002-2002^{-1}}{ln(2002)}.$

Am folosit faptul ca: $2002^{-1}=\frac{1}{2002},ln(2002^{-1})=-ln(2002).$