用分部积分法求不定积分:∫[(1+sinx)/(1+cosx)]*e^x*dx
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用分部积分法求不定积分:∫[(1+sinx)/(1+cosx)]*e^x*dx
用分部积分法求不定积分:∫[(1+sinx)/(1+cosx)]*e^x*dx
用分部积分法求不定积分:∫[(1+sinx)/(1+cosx)]*e^x*dx
∫e^x*(1+sinx)/(1+cosx)dx
=∫e^x/(1+cosx)dx+∫e^xsinx/(1+cosx)dx
=∫e^x/(1+cosx)d+∫sinx/(1+cosx)de^x
=∫e^x/(1+cosx)d+e^xtan(x/2)-∫e^x/(1+cosx)dx (sinx/(1+cosx)=tan(x/2))
=(e^x)tan(x/2) + C