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不定积分的问题
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∫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
=∫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
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追答
其中,你可能要问的,我也写出来
∫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) ∫[(1+sinx)/(1+cosx)]e^xdx =∫e^xdx/(1+cosx)+∫[sinx/(1+cosx)]e^xdx =∫e^xdtan(x/2)+∫tan(x/2)de^x
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