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Let f(x)=(1-x)^2 sin^2 x+x^2 AA xx in...

Let ` f(x)=(1-x)^2 sin^2 x+x^2 AA xx in R ` and Let ` g(x) = int_(1)^(x) ((2 (t-1))/( t+1) - log t ) f(t) dt AA x in [1,oo[`
consider the statement :
There exisits some ` x in R ` such that ` f(x) + 2x = (1+x^2)`

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