Subiectul al III-lea, 2. c)

c) G(x) = ∫₀ˣ f(t) dt = ∫₀ˣ (1 + 2t/(t⁴ + 1)) dt = [t + arctg(t²)]₀ˣ = x + arctg(x²), x ∈ ℝ - 2p ∫₀¹ xG(x) dx = ∫₀¹ (x² + x arctg(x²)) dx = [x³/3]₀¹ + (1/2)∫₀¹ (x²)′ arctg(x²) dx = 1/3 + (1/2)[x² arctg(x²)]₀¹ − ∫₀¹ x³/(x⁴ + 1) dx = = 1/3 + (1/2)·(π/4) − (1/4)[ln(x⁴ + 1)]₀¹ = 1/3 + π/8 − (1/4)ln 2 - 3p