先化简被积函数=(1+2sin(x/2)cos(x/2))/2cos²(x/2)=1/2sec²(x/2)+tan(x/2)故原式=1/2∫sec²(x/2)d(e^x)+∫tan(x/2)d(e^x)=∫e^xd(tan(x/2))+∫tan(x/2)d(e^x)=tan(x/2)e^x+C
=(e^(x)*sin(x))/(cos(x) + 1)+C
