Re: [積分] 請問一題
※ 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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