∫(0->π/2) dx/(1+cos²x)= ∫(0->π/2) dx/(sin²x+cos²x+cos²x)= ∫(0->π/2) dx/(sin²x+2cos²x)= ∫(0->π/2) sec²x/(tan²x+2)= ∫(0->π/2) d(tanx)/(2+tan²x)= (1...