考研 数学 不定积分

2025-01-02 16:26:01
推荐回答(1个)
回答1:

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