依締 asked in 科學數學 · 7 years ago

請問一題微積分的問題

2 Answers

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  • 7 years ago
    Favorite Answer

    Dear Flank, please read:

    圖片參考:http://imgcld.yimg.com/8/n/HA00430218/o/2013081118...

    2013-08-11 18:51:30 補充:

    Please delete the final "=" sign.

  • 7 years ago

    ∫dx/(x^4+4)=∫(dx/x^2 )/(x^2+4/x^2 )=1/4 [∫(1+2/x^2 )dx/((x-2/x)^2+4)-∫(1-2/x^2 )dx/((x+2/x)^2-4)]

    =1/4 [∫d(x-2/x)/((x-2/x)^2+4)-1/4 ∫(1/(x+2/x-2)-1/(x+2/x+2))d(x+2/x) ]

    =1/8 tan^(-1)⁡〖(x-2/x)/2〗-1/16 ln⁡|(x+2/x-2)/(x+2/x+2)|+C

    =1/8 tan^(-1)⁡〖(x^2-2)/2x〗+1/16 ln⁡((x^2+2x+2)/(x^2-2x+2))+C

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