设 x = tanθ。则 dx = sec²θ *dθ。θ = -π/4 → π/4那么，上面的积分变换为：=∫sec²θ*dθ/(1+tan²θ)=∫sec²θ*dθ/sec²θ=∫dθ=θ |θ=-π/4 → π/4=π/4 - (-π/4)=π/2
