高数不定积分求解!∫tanx/(1+cosx)dx=?

Question

高数不定积分求解!
∫tanx/(1+cosx) dx=?

Answer 1

原式=∫sinx/[cosx+(cosx)^2]×dx
=﹣∫1/[cosx+(cosx)^2]×dcosx,
令cosx=t,则原式=﹣∫1/(t+t^2)×dt
=﹣∫[(t+1)-t]/t(t+1)×dt
=﹣∫1/t×dt+∫1/(t+1)×d(t+1)
=ln(t+1)/t+C
=…………