Re: [微積] 分式積分
: 請問各位大大第六題的解法?
: 小弟我用分式積分法做,做到分母是二次式的平方時卡住了。
: (手機排版請見諒。)
你在問下面的積分吧?
dx
∫-----------------
(x^2 + x + 1)^2
8√3 dk
= ∫--------------- k = (2x + 1)/√3
9(k^2 + 1)^2
8√3[sec(u)]^2 du
= ∫-------------------- tan(u) = k
9 [sec(u)]^4
= (2/9)√3[2u + sin(2u)]
(2/√3)(2x+ 1)
= (4/9)√3 arctan((2x + 1)/√3) + (2/9)√3 ---------------------
1 + (1/3)(2x + 1)^2
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推
12/14 00:04, , 1F
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12/14 00:05, , 2F
12/14 00:05, 2F
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12/14 00:10, , 3F
12/14 00:10, 3F
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12/14 00:11, , 4F
12/14 00:11, 4F
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12/14 00:13, , 5F
12/14 00:13, 5F
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12/14 00:14, , 6F
12/14 00:14, 6F
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12/14 09:14, , 7F
12/14 09:14, 7F
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