求∫ex(1+sinx)/(1+cosx)dx,

很有趣的题目：∫e^x(1+sinx)/(1+cosx) dx=∫e^x/(1+sinx) dx+∫e^x*sinx/(1+cosx) dx=∫e^x/[2cos²(x/2)] dx+∫e^x*tan(x/2) dx=∫e^x d[tan(x/2)]+∫e^x*tan(x/2) dx=e^x*tan(x/2)-∫e^x*tan(x/2) dx+∫e^x*t...