Re: [積分] 請問一題

[dunerx0712 (orz)]

※ 引述《GSXSP (Gloria)》之銘言：
: ∫dx/(x^4+1)
: 謝謝



      1                        1                              1
S ___________ dx = S ______________________ dx = S _____________________ dx
     4                   4    2          2                   2      2
  ( x + 1)            ( x +2 x  + 1) -2 x          ( x^2 +1 )  - 2 x

                1
= S ___________________________________  dx

    (x^2 +1 + 2^0.5 x)(x^2 +1 - 2^0.5 x)

      A x + B                 C x+ D
= S _______________ dx + S ___________________  dx
    (x^2 +1 +2^0.5 x)      (x^2 +1 - 2^0.5 x


接下來就用Partial Fraction 就可求解.....
          2
關鍵在於2x 就可以配出來,個人特稱為"無中生有法"......^^...加油吧...


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