=-(1/2)∫(x 1)dx/(x^2 1) ∫dx/x-(1/2)∫dx/(x 1)
=-(1/2)∫xdx/(x^2 1)-(1/2)∫dx/(1 x^2)-lnx-(1/2)ln(x 1)
=-(1/4)∫d(x^2 1)/(x^2 1)-(1/2)arctanx-lnx-(1/2)ln(x 1)
=-(1/4)ln(1 x^2)-lnx-(1/2)ln(x 1)-(1/2)arctanx c
=-ln[(1 x^2)^(1/4)*x*(x 1)^(1/2)]-(1/2)arctanx c.