M1 integrals數學題?10點

2011-12-10 7:17 am
1.
圖片參考:http://hk.knowledge.yahoo.com/math//symbols/integral.gif
1/(1-(1-x)^1/2)dx

2.u=(x+1)/(x-1),find
圖片參考:http://hk.knowledge.yahoo.com/math//symbols/integral.gif
1/((x+1)(x-1))dx
更新1:

answers:1.2(1-x)^1/2+2ln(1-x)^1/2-1)+C 2.1/2ln((x-1)/(x+1))+C

更新2:

u^2=1-x then2u=-x why is 2udu=-dx

更新3:

u^2=1-x then2u=-1才對 why is 2udu=-dx second last ln(u)=ln((x+1)/(x-1)) why is ln((x-1)/(x+1))

回答 (1)

2011-12-10 6:38 pm
✔ 最佳答案
http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-1674.jpg

圖片參考:http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-1674.jpg


2011-12-11 13:39:20 補充:
Careless mistake corrected:
http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-1745.jpg

2011-12-11 21:50:07 補充:
u^2 = 1 - x
d/dx u^2 = d/dx (1-x)
2u (du/dx) = -1
2u du = - dx

2011-12-11 21:51:59 補充:
- ln u = ln (1/u)
So - ln u = ln (x-1)/(x+1)


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