求s(积分号)e^x*(1+sinx)/(1+cosx) dx,

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求s(积分号)e^x*(1+sinx)/(1+cosx) dx,
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求s(积分号)e^x*(1+sinx)/(1+cosx) dx,
求s(积分号)e^x*(1+sinx)/(1+cosx) dx,

求s(积分号)e^x*(1+sinx)/(1+cosx) dx,
∫e^x(1+sinx)dx/(1+cosx)
=∫e^xdx/(1+cosx)+∫e^xsinxdx/(1+cosx)
1+cosx=2cos(x/2)^2 sinx/(1+cosx)=tan(x/2)
=∫e^xd(x/2)/cos(x/2)^2+∫e^xtan(x/2)dx
=∫e^xdtan(x/2)+∫tan(x/2)de^x
=e^xtan(x/2)+C

S e^x(1+sinx)/(1+cosx) dx
=(1/2)S e^x[{(sec(x/2)}^2 + 2tan(x/2)] dx
= S e^xtan(x/2) dx + S e^x{(sec(x/2)}^2 d(x/2 )
=e^x tan(x/2) - S e^x dtan(x/2) + S e^x dtan(x/2) +C
=e^x tan(x/2)+C