求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,

求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,
求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,

求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,
∫ (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

∫(1+2x^2)/[x^2*(1+x^2)]dx
=∫(1+x^2+x²)/[x^2*(1+x^2)]dx
=∫(1/(1+x^2)+1/[x^2]dx
=arctanx-1/x+c

dx?

目测吧 孩子！！！