kill(all);

depends(y,x);

diff(y,x)=y/(x+sqrt(y^2-x^2));

'integrate('y/'(x+sqrt(y^2-x^2)),x) =
(1/4)*y*(log(2*x^2-y^2) + 2*atan(x/sqrt(y^2-x^2))+2*atanh(x/sqrt(y^2-x^2)));

'integrate('y/'(x+sqrt(y^2-x^2)),y)=
ratsimp(integrate(y/(x+sqrt(y^2-x^2)),y));