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Partial Fraction Decomposition

  1. Jun 21, 2013 #1
    Hello I am stuck on an ODE involving substitution. I have done the correct substitutions, but have become stuck on decomposing the fraction.
    i have the following

    ∫(1/x)dx + ∫(u+1)/(u^2+1)du = 0

    Im stuck on breaking the u down into a partial decomposition. Could anyone offer some advice on how to start decomposing this bad boy?

    Thanks
     
  2. jcsd
  3. Jun 21, 2013 #2
    You don't need to decompose that with partial fractions.
    Split up the (u+1)/(u^2+1) as u/(u^2 + 1) + 1/(u^2+1).
    Now you can do a substitution on the 1st term and the 2nd term is just arctan(u).
    I'm not even sure that you could do a partial fraction decomposition on that because you can't factor the denominator.
     
  4. Jun 22, 2013 #3
    I see, thanks for pointing that out! I'm do for an algebra review it seems :)
     
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