求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,
问题描述：
求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,
答
∫ (1+2x²)/[x²(1+x²)] dx
=∫ [(1/x²)+1/(1+x²)]dx
=∫ (1/x²) dx+∫ 1/(1+x²) dx
=-1/x+arctanx+C
C为任意常数