∫1/(x2 x 1)2dx
=∫1/[(x 1/2)2 3/4]2dx
令x 1/2=√3/2*tanθ,dx=√3/2*sec2θdθ
sinθ=(x 1/2)/√(x2 x 1),cosθ=(√3/2)/√(x2 x 1)
原式=(√3/2)∫sec2θ/(3/4*sec2θ)2dθ
=(√3/2)(16/9)∫sec2θ/sec?θdθ
=8/(3√3)*∫cos2θdθ
=4/(3√3)*∫(1 cos2θ)dθ
=4/(3√3)*(θ 1/2*sin2θ) C
=4/(3√3)*arctan[(2x 1)/√3] (2x 1)/[3(x2 x 1)] C