Re: [積分] very難

[LuisSantos ( )]

※ 引述《chingyes (axsazxc)》之銘言：
: http://0rz.tw/5b5bZ
: 請問紅線部分
: 如何變過去的
: 請神人指導@@

           x - 1          A     Bx + C
1. 令   ------------  =  --- + ---------
        (x)(x^2 + 1)      x     x^2 + 1


   則 x - 1 = (A)(x^2 + 1) + (x)(Bx + C)

            = (A + B)(x^2) + Cx + A

   A + B = 0       A = -1

   C = 1       =>  B = 1

   A = -1          C = 1



          x - 1       A      B        C
2. 令 ------------ = --- + ----- + -------
      (x^2)(x + 1)    x     x^2     x + 1


   則 x - 1 = (A)(x)(x + 1) + (B)(x + 1) + (C)(x^2)

            = (A + C)(x^2) + (A + B)(x) + B

   A + C = 0      A = 2

   A + B = 1   => B = -1

   B = -1         C = -2




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◆ From: 140.119.129.141
推 chingyes:如何知道要分 X 跟 X^2
→ LuisSantos:這一般的微積分教科書都有寫
推 zptdaniel:分母@@
→ zptdaniel:這是劃分項分式
推 chingyes:啥碗糕@@
推 sexysam:回1樓 因為X^2的分子可能為AX+B
→ sexysam:再拆開就變成X和X^2兩項