1.原式=1/2∫ln(x-1)d(x^2)=1/2x^2ln(x-1)-1/2∫x^2/(x-1)dx=1/2x^2ln(x-1)-1/2∫(x^2-x+x-1+1)/(x-1)dx=1/2x^2ln(x-1)-1/2∫xdx-1/2∫dx-1/2∫dx/(x-1)=1/2x^2ln(x-1)-1/4x^2-1/2x-1/2ln(x-1)+C
2.两边对x求导:1+1/(y^2+1)*y'=y'
y'=(y^2+1)/y^2=1+1/y^2
在对x求导:y''=1-2/y^3*y'=1-2/y^3*(1+1/y^2)=1-2/y^3-2/y^5