作者Highhuman (Ryan)
看板trans_math
標題[積分] 反三角積分
時間Sun Jul 1 00:52:35 2012
1
∫x*arctan(x^2) dx =_____.
0
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※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 111.249.229.110
1F：→ a016258:...... u=x^2 ~ 114.42.183.69 07/01 01:00
2F：→ Highhuman:我是最後卡住...111.249.229.110 07/01 01:06
3F：→ Highhuman:(1/2)∫arctan(u) du = ...111.249.229.110 07/01 01:09
4F：推 fb74123698:h=arctanu,dk=du 114.38.245.223 07/01 01:15
5F：→ Highhuman:dk=du ?!111.249.229.110 07/01 01:18
6F：→ fb74123698:dh=1/(1+x^2),k=u..像uv-∫vdu 114.38.245.223 07/01 01:21
7F：→ Highhuman:不過用分部積分，似乎沒辦法消掉arctan111.249.229.110 07/01 01:27
8F：→ Highhuman:hk-∫kdh = arctan(u)/1+x^2-∫kdh111.249.229.110 07/01 01:28
9F：→ fb74123698:=>uarctanu-∫u/(1+u^2)du..應該吧QQ 114.38.245.223 07/01 01:31
10F：→ Highhuman:更正:hk-∫kdh = u*arctan(u)-∫kdh111.249.229.110 07/01 01:32
11F：→ Highhuman:阿...你算算看囉~ 真的算得出來嗎?! = =111.249.229.110 07/01 01:34
12F：推 fb74123698:∫kdh那邊就可以積了吧,我還沒帶0,1進 114.38.245.223 07/01 01:35
13F：→ fb74123698:去的說 114.38.245.223 07/01 01:35
14F：→ Highhuman:嗯嗯 好像可以耶~111.249.229.110 07/01 01:38
15F：→ Highhuman:答案是:(pi/4)-(ln2/2)嗎?!111.249.229.110 07/01 01:43
16F：→ fb74123698:我比你多一個1/2,會不會剛開始那邊 114.38.245.223 07/01 01:49
17F：→ Highhuman:成大100解答哪裡有阿?!111.249.229.110 07/01 01:52
18F：→ fb74123698:原來是成大100=.=自己做過自己都忘記 114.38.245.223 07/01 01:54
19F：→ Highhuman:所以是(1/2)[pi/4)-(ln2/2)]這樣囉~111.249.229.110 07/01 01:55
20F：→ fb74123698:答案是 pi/8 - (ln2)/4 114.38.245.223 07/01 01:55
21F：→ fb74123698:嗯嗯對 114.38.245.223 07/01 01:56
22F：→ Highhuman:晚上算微積分算到快趴了...@@111.249.229.110 07/01 01:57
23F：→ Highhuman:可以提供成大100嗎?! 0..0111.249.229.110 07/01 01:58
24F：→ fb74123698:真的!!!血糖太低T^T 114.38.245.223 07/01 01:58
25F：→ fb74123698:你要哪幾題.. 114.38.245.223 07/01 01:59
26F：→ Highhuman:冏了...這題不難...卻卡了這麼久...@@111.249.229.110 07/01 02:00
27F：→ fb74123698:我也常降..超囧 114.38.245.223 07/01 02:01
28F：→ Highhuman:可以的話都給吧~考試逼近....急需~111.249.229.110 07/01 02:01
29F：→ Highhuman:轉板上互相幫忙...感覺真得很溫馨...111.249.229.110 07/01 02:02
30F：→ fb74123698:1a:DNE1b:e^-1/2.3a:2ln(ln4)-2ln(ln2) 114.38.245.223 07/01 02:05
31F：→ fb74123698:6:1/(2pi)。7:ln|y/x| 114.38.245.223 07/01 02:08
32F：→ fb74123698:8:dmin=5^(1/2)發生在(x,y)=(+-1,+-2) 114.38.245.223 07/01 02:10
33F：→ fb74123698:4:[243/28+3/2-1/12-1/252-1/18+1/4]pi 114.38.245.223 07/01 02:13
34F：→ Highhuman:謝謝哟~ 一起甲幼吧!!111.249.229.110 07/01 03:01