令x=cost则原式=∫√(1-cost)/(1+cost)dcost=∫√(1-cos^2t)/(1+cost)^2dcost∫-sin^2t/(1+cost)dt=∫(cos^2t-1)/(1+cost)dt=∫cost-1dt=-sint-t+c=-√(1-x^2) - arccost + c