∵∫e^y*cosydy=e^y*(cosy+siny)/2+C (C是积分常数)∴ ∫e^(arctanx)dx/(x²+1)^(3/2)=∫e^y*sec²ydy/sec³y (令y=arctanx,则cosy=1/√(x²+1),siny=x/√(x²+1))=∫e^y*cosydy=e^y*(cosy+siny...