Re: [理工] 求此積分過程

[Honor1984 (希望願望成真)]

※ 引述《xoo1208 (RaInBoW)》之銘言：
: https://www.dropbox.com/s/zl7062b5u63iheu/Questions2.jpg
: 求此積分過程 ~~



      exp(∫(1-x^2)^(-1) d(1-x^2))
= x∫--------------------------------  dx
      x^2

            1
= x∫ -------------- dx
        x^2 (1-x^2)


1/(x^2(1-x^2)) = 1/x^2 + 1/(1-x^2)

               = 1/x^2 +  (1/2)[1/(1-x) + 1/(1+x)]

= x [(-1/x) + (1/2)ln[(x+1)/(1-x)]]

= -1 + (x/2)ln[(x+1)/(1-x)]

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推 xoo1208:exp裡面是先用變數變換代換嗎 ?
→ Honor1984:對
→ xoo1208:謝謝大大~~