设x=tanθ ,0=<θ<=π/4 x^2/(1+x^2)^2=(tanθ)^2*(cosθ)^4=(sinθ)^2(cosθ)^2 dx=dtanθ=dθ/(cosθ)^2 所以原式=∫(sinθ)^2dθ=π/8 -1/4
