∫e^xdx/(1+cosx)+∫e^xsinxdx/(1+cosx)
=∫e^xdtan(x/2)+∫tan(x/2)de^x
=e^x tan(x/2) -∫tan(x/2)de^x+∫tan(x/2)de^x+C
=e^x tan(x/2) +C
其中∫dx/(1+cosx)=∫dx/2cos(x/2)^2=∫sec(x/2)^2d(x/2)=∫dtan(x/2)
sinx/(1+cosx)=2sin(x/2)cos(x/2)/(2cos(x/2)^2)=tan(x/2)
高等数学:求不定积分(答案提示用回旋法做)