大一高数有理函数的积分为什么第一个到右边成了三个而第二个只变成了两个,有什么区别

2025-06-26 11:52:25
推荐回答(1个)
回答1:

(2x²+2x+13)/[(x-2)(x²+1)²]
=A/(x-2)+(Bx+C)/ (x²+1)²+(Dx+E)/ (x²+1)
A/(x-2)+[Bx+C+(Dx+E)(x²+1)]/(x²+1)²

(x-3)/[(x-1)²(x+1)]=(Ax+B)/(x-1)²+C/(x+1)
=(Ax+A-A+B)/(x-1)²+C/(x+1)
=A/(x-1)+(-A+B)/(x-1)²+C/(x+1)