∫₁² ln(1 + 2/x) dx =
= ∫₁² 1•ln(1 + 2/x) dx
= ∫₁² x'•ln(1 + 2/x) dx
(Folosesc integrarea prin părți:
∫ f'•g dx = f•g - ∫ f•g' dx)
= x•ln(1 + 2/x) |₁² - ∫₁² x•[ln(1 + 2/x)]' dx
= 2ln2 - ln3 - ∫₁² x•(-2/x²)/(1 + 2/x) dx
= ln4 - ln3 + ∫₁² 2/(x+2) dx
= ln(4/3) + 2∫₁² 1/(x+2) dx
= ln(4/3) + 2∫₁² (x+2)'/(x+2) dx
= ln(4/3) + 2ln(x+2)|₁²
= ln(4/3) + 2ln(4) - 2ln(3)
= ln(4/3) + 2ln(4/3)
= 3ln(4/3)
