How Can the Integral Be Simplified for Easier Evaluation?

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mathwizarddud
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Evaluate

[tex]A \ = \ \int_{0}^{1} \frac{ 4x \ + \ 3 }{ ( x^2 - x +1 )^{2} } dx[/tex]
 
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Express the numerator in such terms that it has some relation to the denominator plus some constants.