积分:(x^2+1)/(x^4+1)dx=积分:(1+1/x^2)/(x^2+1/x^2)dx(上下同时除以x^2)=积分:d(x-1/x)/[(x-1/x)^2+(根号2)^2]=1/根号2*arctan[(x-1/x)/根号2]+C=1/根号2*arctan[(x^2-1)/(x根号2)]+C(C为常数)
=1/{√2*tan(√2*x+1)}-1/{√2*tan(1-√2*x)}+C
