∫1/(1+cos t)dt

题目

∫1/(1+cos t)dt

答案

∫ 1/(1+cost) dt
= ∫ (1-cost)/[(1+cost)(1-cost)] dt
= ∫ (1-cost)/sin²t dt
= ∫ csc²t dt - ∫ csct*cott dt
= -cot(t) + csc(t) + C