x/x^2-x+1的积分推导

Question

x/x^2-x+1的积分推导

Answer 1

y=(x^2-x+1)/(x^2+x+1)化为(y-1)x^2+(y+1)x+y-1=0
y=x^2-x+1/x^2+x+1的分母x^2+x+1=(x+1/2)^2+3/4>0所以x属于R均使y有意义,
说明此方程(把y看做普通的系数)对于任何的实数R,都有解,所以 判别式就大于等于0