∫(0→π/2) dx/(1 + cos²x)= ∫(0→π/2) dx/[1 + (1 + cos2x)/2]= 2∫(0→π/2) dx/(3 + cos2x),θ = 2x= ∫(0→π) dθ/(3 + cosθ)= ∫(0→π) dθ/[3sin²(θ/2) + 3cos²(θ/2) + cos²(θ/2...