Question

求t/(1+cost)的不定积分 求定积分t/(1+cost)，上限π/2,下限是2π/3

Answer 1

∫t/(1+cost) dt
=2∫t [sec(t/2)]^2 dt
=∫ tdtan(t/2)
= ttan(t/2) - ∫ tan(t/2) dt
= ttan(t/2) - ∫ sin(t/2)/cos(t/2)dt
= ttan(t/2) + 2 ln|cos(t/2)|+ C