d/drho (-)*log(b*rho-1) = (-)*1/(b*rho-1)*b = b/(1-b*rho) = q1
so it is correct. But your result is correct as well.
Ignoring the (-) in front for the moment, your result is
log(1-b*rho) = log((-1)*(b*rho-1)) = log(b*rho-1) + log(-1)
= log(b*rho-1) +i*pi
which differs from the 'int' result by a constant of integration i*pi. Whichever result you want to use would usually be decided by keeping the argument of the log function to be positive.