作者dunerx0712 (orz)
看板trans_math
标题Re: [积分] 请问一题
时间Thu Jan 6 00:50:29 2005
※ 引述《GSXSP (Gloria)》之铭言：
: ∫dx/(x^4+1)
: 谢谢
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
接下来就用Partial Fraction 就可求解.....
2
关键在於2x 就可以配出来,个人特称为"无中生有法"......^^...加油吧...
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