Subiectul al III-lea, 2. c)

c) ∫₁ᵉ (f(x) − 2/(x + 1)) · ln² x dx = ∫₁ᵉ 6x ln² x dx = ∫₁ᵉ (3x²)′ ln² x dx = [3x² ln² x]₁ᵉ − ∫₁ᵉ 6x ln x dx = = 3e² − [3x² ln x]₁ᵉ + [3x²/2]₁ᵉ = 3(e² − 1)/2 - 3p 3(e² − 1)/2 = a(e² − 1)/2, de unde obținem a = 3 - 2p