∫2x^2/(x^2+1) 怎么等于2x +∫2/(x^2+1)dx 后面那个2x +是怎么来的
问题描述：
∫2x^2/(x^2+1) 怎么等于2x +∫2/(x^2+1)dx 后面那个2x +是怎么来的
答
2x^2/(x^2+1)
=(2x^2+2-2)/(x^2+1)
=[2(x^2+1)-2]/(x^2+1)
=2(x^2+1)/(x^2+1)-2/(x^2+1)
=2-2/(x^2+1)
所以原式=∫2dx-∫2dx/(x^2+1)
=2x-∫2dx/(x^2+1)
=2x-2arctanx+C