设t=tan(x/2),则dx=2dt/(1+t²),sin(x/2)=t/√(1+t²),cos(x/2)=1/√(1+t²) 于是,原式=1/4∫(2,tan(π/8))(1+2/t²+1/t^4)dt =1/4(t-2/t-(1/3)/t³)│(2,tan(π...