Subiectul al III-lea, 2. c)

2.c) ∫₁ᵉ (f(x)√x ln x)/(x+1) dx = ∫₁ᵉ x ln x dx = ∫₁ᵉ (x²/2)′ ln x dx = [(x²/2) ln x]₁ᵉ − ∫₁ᵉ (x²/2)·(1/x) dx = e²/2 − (1/2)∫₁ᵉ x dx = - 3p = e²/2 − (1/2)[x²/2]₁ᵉ = e²/2 − e²/4 + 1/4 = (e²+1)/4, deci a = 1 - 2p