∫1/(1+cos t)dt

∫1/(1+cos t)dt

∫1/(1+cost)dt
=∫(1-cost)/[(1+cost)(1-cost)] dt
=∫(1-cost)/sin²;t dt
=∫csc²;t dt -∫csct*cott dt
= -cot(t)+ csc(t)+ C