∫1/[x(x^2+1)] dx,d(x^2)=2xdx=(1/2)∫1/[x^2*(x^2+1)] d(x^2)=(1/2)∫1/x^2 d(x^2)-(1/2)∫1/(x^2+1) d(x^2)=(1/2)∫1/x^2 d(x^2)-(1/2)∫1/(x^2+1) d(x^2+1)=(1/2)ln(x^2)-(1/2)ln(x^2+1)+C=(1/2)ln[x^2/(x^2+1)]...