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
为什么直接变成了 ∫[1/x²+1/(1+x²)]dx 1+2x^2 哪里去了?
答
(1+2x^2)/[x^2*(1+x^2)]
=(1+x^2+x^2)/[x^2*(1+x^2)]
=(1+x^2)/[x^2*(1+x^2)]+x^2/[x^2*(1+x^2)]
=1/x^2+1/(1+x^2)
所以原式=-1/x+arctanx+C