∫[(1+sinx)/(1+cosx)]*(e^x)dx
问题描述：
∫[(1+sinx)/(1+cosx)]*(e^x)dx
答
∫[(1+sinx)/(1+cosx)]*(e^x)dx=∫[ (1+2sin(x/2)cos(x/2)) / (2cos²(x/2)) ]*(e^x)dx=∫[ (1/2)sec²(x/2)+tan(x/2) ]*(e^x)dx=(1/2)∫ sec²(x/2)e^x dx+ ∫ (e^x)tan(x/2) dx=∫ sec²(x/2)e^x ...