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Anti-derivative problem help

  1. Dec 1, 2005 #1
    find the anti-derivative of :

    f(x) = 4 - 3(1+x^2)^(-1)

    I have thought this question for hours....but no clue at all....

    that is what I have attempted:

    F(x) = 4x - 3 Ln(1 + x^2) ....
    but if i differentiated it ---
    then I got F'(x) = 4 - 3*(2x)/(1 + x^2).....

    is there anyway to eliminate the (2x) ...?

    please help
     
  2. jcsd
  3. Dec 1, 2005 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Well, first the "4" is obvious- you are completely correct that it's anti-derivative is 4x.

    Now, for 3/(1+ x^2). Log doesn't work because 1+ x^2 is not x!

    Do you know the derivative of arctan(x)?
     
  4. Dec 1, 2005 #3
    oh....thank you....
    I totally forgot about there are some formular for that....
    yes....
    so is the answer 4x - 3 arc tan x + C?
     
  5. Dec 1, 2005 #4
    but in my text book, i can not find the prove of those identities...
    just wonder if there is any link for that...
     
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