∫[(3x^4+2x^2)/(x^2+1)]dx=∫3x^2dx-∫dx+∫1/(x^2+1)dx请问这个是怎么变化的?在百度上也找到解法了但是看不懂

Question

∫[(3x^4+2x^2)/(x^2+1)]dx = ∫3x^2dx - ∫dx + ∫1/(x^2+1)dx 请问这个是怎么变化的?
在百度上也找到解法了但是看不懂

Answer 1

3x^4+2x^2 = 3x^2(x^2+1) +x^2
= 3x^2(x^2+1) -(x^2+1) +1
(3x^4+2x^2)/(x^2+1) =[3x^2(x^2+1) +(x^2+1) -1]/(x^2+1)
=3x^2 -1 + [1/(x^2+1)]
∫[(3x^4+2x^2)/(x^2+1)]dx = ∫3x^2dx - ∫dx + ∫1/(x^2+1)dx