∫ 1/(1 + cost) dt,cos2t = 2cos²t - 1 ==> cost = 2cos²(t/2) - 1
= ∫ 1/[2cos²(t/2)] dt
= ∫ sec²(t/2) d(t/2)
= tan(t/2) + C
= sint/(1 + cost) + C