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Homework Help: Anti derivative problem

  1. Nov 1, 2008 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    3. The attempt at a solution

    I attempted to bring the denominator up using (1+x^2)^-1 and i also tried long division to simplify but had no luck...

    1/(1+x^2) is the inverse tan derivative, but what can i do from here:

    (2+x^2) * 1/(1+x^2) is substitution legal here?
    Last edited: Nov 1, 2008
  2. jcsd
  3. Nov 1, 2008 #2


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    Homework Helper

    Try putting (2+x^2)/(1+x^2) as 2/(1+x^2) + x^2/(1+x^2)

    then divide out the second fraction
  4. Nov 1, 2008 #3


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    Science Advisor

    Or write
    [tex]\frac{2+x^2}{1+ x^2}= \frac{1}{1+x^2}+ \frac{1+ x^2}{1+ x^2}[/tex]
  5. Nov 1, 2008 #4
    so i would cancel the second term then take the anti derivate to be left with invesre tan of x + x + C .. is this correct?
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