换元法：
t=tanx/2 dx=2/1+t^2 dt
cosx=1-t^2/1+t^2 x=2arctant
原式=∫2arctantdt=2t arctant-∫2t/(1+t^2)dt
=2tarctant-ln(t^2+1)+c
=xtanx/2-ln(1+(tanx/2)^2)+c
换元法：
t=tanx/2 dx=2/1+t^2 dt
cosx=1-t^2/1+t^2 x=2arctant
原式=∫2arctantdt=2t arctant-∫2t/(1+t^2)dt
=2tarctant-ln(t^2+1)+c
=xtanx/2-ln(1+(tanx/2)^2)+c