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Hard integral 2

  1. Mar 11, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]
    \int_0^1 \frac{x^4(1-x)^4}{1+x^2}\ dx
    [/tex]

    3. The attempt at a solution
    A gonio substitution gets nasty really fast moreover the differentiation under the integral sign trick doesn't seem to give more insight (at least that's what I think). Integration by parts gets a ln(.) times something nasty. The boundaries suggest a series expansion or a smart substitution...

    Can someone give me a hint?
     
  2. jcsd
  3. Mar 11, 2009 #2
    divide the two polinomials
    and youll get an easier integral
     
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