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Simple integration

  1. Jun 15, 2017 #1
    1. The problem statement, all variables and given/known data
    Integrate: [(x^4+x^2+1)/2(1+x^2)]dx

    2. Relevant equations

    Integral of x^n=x^(n+1)/(n+1)
    Integral of 1/(1+x^2)=arctanx
    3. The attempt at a solution
    I have attached my solution.All the steps seem to be correct,but the answer isn't matching,don't know why.
     

    Attached Files:

  2. jcsd
  3. Jun 15, 2017 #2
    Your integration from lines 3 to 4 is not correct:
    [tex]
    \int \frac{1}{1 + x^{-2}} \mathrm{d} x \neq \tan^{-1} \left(\frac{1}{x}\right).
    [/tex]
    My suggestion is to instead split the original expression as
    [tex]
    \frac{x^4 + x^2 + 1}{2(1 + x^{2})} = \frac{x^4 + x^2}{2(1 + x^{2})} + \frac{1}{2(1 + x^{2})}.
    [/tex]
     
  4. Jun 15, 2017 #3
    Oops,why didn't I think of that?Thanks.
    Yep,sorry.
     
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