\(dy/(y^2-1)= dx/(x^2-1)\)

\(\int dy/y^2-1= \int dx/(x^2-1)\)

\(\int dy/((y-1)(y+1))= \int dx/((x-1)(x+1))\)

\(1/2 \int dy/(y-1)-1/2 \int dy/(y+1)= 1/2 \int dx/(x-1)-1/2 \int dx/(x+1)\)

\(1/2 \ln(y-1)-1/2 \ln(y+1)= 1/2 \ln(x-1)-1/2 \ln(x+1)+C\)

\(1/2 \ln((y-1)/(y+1))= 1/2 \ln ((x-1)/(x+1))+C\)

\(\ln ((y-1)/(y+1))= \ln ((x-1)/(x+1))+C\)