设t=x 1/2,则x^2 x 1=t^2 3/4
-x^2-2=-(t-1/2)^2-2=-t^2 t-9/4
原式=∫[-1/(t^2 3/4) (t-3/2)/(t^2 3/4)^2]dt
=(-2/√3)arctan(2t/√3)-1/[2(t^2 3/4)]-(3/2)2t/[3(t^2 3/4)] 4/(3√3)*arctan(2t/√3) c
=(-4/√3)arctan(2t/√3)-(1 2t)/[2(t^2 3/4)] c
=(-4/√3)arctan[(2x 1)/√3]-(x 1)/(x^2 x 1) c