作者kk990366 (kk990366)
看板trans_math
標題[考古] 84年台大瑕積分
時間Tue Apr 28 18:52:39 2009
00 x - 1
S -------------- dx = ?
1 4 3 2
x + x + x + x
00為無窮大
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◆ From: 118.168.76.49
1F：推 Frobenius:x^4+x^3+x^2+x = x(x^3+x^2+x+1) =122.124.157.144 04/28 19:06
2F：→ Frobenius:x(x+1)(x^2+1) 再部分分式122.124.157.144 04/28 19:07
3F：推 Frobenius:1/(1+x^2) + 1/(1+x) - 1/x122.124.157.144 04/28 19:09
4F：推 Frobenius:得ArcTan(x) + ㏑| (1+x)/x | + C122.124.157.144 04/28 19:12
5F：推 Frobenius:上式趨近∞得π/2；代入1得π/4 + ㏑2122.124.157.144 04/28 19:16
6F：推 Frobenius:上下限相減等於π/4 - ㏑2122.124.157.144 04/28 19:18