求(x^2+1)/(x^4+1)的不定积分
问题描述：
求(x^2+1)/(x^4+1)的不定积分
答
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)...