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Find the anti derivative of f'(x)= (2+x^2)/(1+x^2)

  1. Nov 25, 2011 #1
    1. The problem statement, all variables and given/known data

    f'(x)= (2+x^2)/(1+x^2), find f(x).

    2. Relevant equations



    3. The attempt at a solution

    I am pretty sure you have to use integration by parts... but I don't think we learned it yet. Is there a way to do this without using integration by parts? If not, how would I use integration by parts for his question?
     
  2. jcsd
  3. Nov 25, 2011 #2

    gb7nash

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    Well, [itex]\frac{2+x^2}{1+x^2} = \frac{2}{1+x^2}+\frac{x^2}{1+x^2}[/itex]

    If you know what the integral of [itex]\frac{1}{1+x^2}[/itex] is, the first part is easy. The second part is simple as well, if you recognize what to do first before integrating.
     
  4. Nov 25, 2011 #3

    Ray Vickson

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    You could also write [tex] \frac{2+x^2}{1+x^2} = 1 + \frac{1}{1+x^2}. [/tex]

    RGV
     
  5. Nov 26, 2011 #4
    Thank you to both of you for your help, both of you helped me solve this and other similar questions.
     
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